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Smooth Bilevel Programming for Sparse Regularization

Smooth Bilevel Programming for Sparse Regularization

Talk given at the SMAI-SIGMA workshop in Paris.

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Gabriel Peyré

October 19, 2021
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  1. Smooth Bilevel Programming for Sparse Regularization Gabriel Peyré É C

    O L E N O R M A L E S U P É R I E U R E RESEARCH UNIVERSITY PARIS Joint work with: Clarice Poon 
 (Bath University)
  2. k2 with > 0. P i ⌘ i . Quadratic

    Variational Forms Bilevel VarPro
  3. Sparse Regularization <latexit 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min

    x2Rd 1 2 kAx yk2 + kxk1 <latexit 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min Ax=y kxk1 <latexit 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Ax ⇡ y <latexit 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over-determined + noise <latexit sha1_base64="KP+hZOSsydxfXbMgjqAFx8TV0IU=">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</latexit> under-determined <latexit sha1_base64="nCIFL0QNopmQRSBhYa6iV/R4B74=">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</latexit> regularize
  4. Sparse Regularization <latexit 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A 2 Rn⇥d <latexit 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min

    x2Rd 1 2 kAx yk2 + kxk1 <latexit 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min Ax=y kxk1 <latexit 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Ax ⇡ y <latexit 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over-determined + noise <latexit sha1_base64="KP+hZOSsydxfXbMgjqAFx8TV0IU=">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</latexit> under-determined <latexit sha1_base64="nCIFL0QNopmQRSBhYa6iV/R4B74=">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</latexit> regularize <latexit 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Spike deconvolution: <latexit 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Ax = a ? x <latexit 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x0 <latexit 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y = x ? a + " <latexit 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x
  5. Sparse Regularization <latexit 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A 2 Rn⇥d <latexit 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min

    x2Rd 1 2 kAx yk2 + kxk1 <latexit 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min Ax=y kxk1 <latexit 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Ax ⇡ y <latexit 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over-determined + noise <latexit sha1_base64="KP+hZOSsydxfXbMgjqAFx8TV0IU=">AABB03ictVzdchTHFW6cHxvyY0guczOJTAqnMBYyFcflSpWFJISMAMGuBLYF1P6MloXZnWVmVwLWuknlNo+Q2+Qx8hx5g+Qqr5Dz0z3ds9szp0chdEnq6e3vnNNnuk+fc7qX7iQZ5tPV1X+ee+8HP/zRj9//4PyFn/z0Zz//8OKlXxzk6Szrxfu9NEmzx91OHifDcbw/HU6T+PEkizujbhI/6r7cwM8fHcdZPkzH7embSfxk1BmMh0fDXmcKTc8uXpqN+3H2ST+extkIaPSjZxdXVq+t0r9ouXJdV1aU/reXXor21aHqq1T11EyNVKzGagr1RHVUDuU7dV2tqgm0PVFzaMugNqTPY3WqLgB2Br1i6NGB1pfwewBP3+nWMTwjzZzQPeCSwE8GyEhdBkwK/TKoI7eIPp8RZWytoj0nmijbG/jb1bRG0DpVz6FVwpmeoTgcy1QdqT/QGIYwpgm14Oh6msqMtIKSR86opkBhAm1Y78PnGdR7hDR6jgiT09hRtx36/F/UE1vxuaf7ztS/ScrLUCLV0qNPCwoddUz0I3qbM/iM5UmA8wAoxHqMWDshXY9o9GPoP4f2e1BOqWZ00oUyp9bTWuQGFB9yQ0RuQ/Eht0XkLhQfcldE7kHxIfc0ErEZ6dyPb0Hx4Vsi5wdQfMgHIvIhFB/yoYg8gOJDHojIb6H4kN+KyFtQfMhbIvIOFB/yjohsQ/Eh2yJyH4oPuS8it6D4kFsaWb1SMygp0RkKq3Id6mUeaCkSaFkX5btJ1tGHvRmwpnsVWHlVb8JfP3YzQKdxBXYrYN4dVWDlmbcNNtKPlW3RbdpNfNjbInYHZoAfuyNiv1YvKrBfB6y0lxVYea3tQj8/Vra+d+HJj70rYu9BzY+V96j70OLH3g/YMSYV2D0R+0C9qsCGWP2sAivb/RbYFT9W3qfa0N+PDbGmswqsbE8PwIPxY+Xd6hG0+rGPROxj9boC+1jEfgPW3Y/9JmCHfVuBNXvsBdpBBuSPxLBi66h1ilWJtQlQ6wj8k2JvScg37kK7hBkUmAFhRiJiu0BsByJ2C8RusFx5YUdz8ndlLq0C0QpEdIu9CWtTsX+/6I+1JACxWSA2FxB1Him+azOWY/IuTIuEnBY7F9ZCxpQW9htrsZ4P9ZbXIO6XEDy3n9PMv0rREkZQqKk6as+LPZ6RET3XIU4oejOjNDxk3LSwCi7qtYjqelBdEfXGg3ojomYe1ExEHXtQxyLKrnwXdxgwA6z+8V3M6YlnAPvI1SUCr2Addp3bsEYjmD974AU+pJb78LdFsbdU6iTDaB73ScxyPClZ4gxqc7UC7TYq3KT4OqEVFoNk3PO+jvHxCXMbc73m2AqfFjt5VGRMwukMSZ5BQQe9xYjWUzM6d6jllLw7rjXD3y7Wvak1w2+Rxk/Ji+daM/xUSz89g+xtjW2fAduC1TTR2rf1pjQ4/8I0TP0C7bpocfGtjvScQXqvG9Lf0W9m5wzvZYNqrB9bb0Yjd8aXl8bXhIbVc+7ouRkV9J7Y6zW1qPFIxjrutfWmMqS0i461HPap6ZvBPn39Zky9GY098Lg2KOaeO/Wms3dSjMbWm9E4UJz3PCVP3tSb0RjQM+vD1pvRwGxLR8f5tt7UsqMGOHa29aZWfUxZYMwB8ZznFusVZeQnzTS1IfkH9dka1+df3scwZ/O0iBHqKVnftppOt9jL6iUy/kIMVm3aUA70L2aOD1amMVdrYnzFMkxL+/syHbvHo+Z3QYsRrH4+A5By5glIaHISaL0ToHhdjLrKIzO4NRGHs+RoAXWoW6eit2j5ctao3PaMWqW4zI7W6vGQ7HVOc29CPuEuaVbSw27lG66iKGlot6QhmV4T3b3V67Ws/VURN1lATIqZ1qMTIT5Jq49TfVpvOTq+rE95plD4zMfOX8w2H2lrgzFPSrYIZanj6fYzeSS3DffVq8rmuPmziN4o2qtjshpDOpHKxSjUZIvZG5/Ts6W9T2dyyINp9OA9RprKRPGpGWbRMZ8ekUV17a3EG/VlMnRcz8nqGntcjx446IEH3TzG2YAd4x7U2hAz7MNTOyDKuVDoKiWNZ+qT4nQ0pTdYH9EnJQtpaLC9iUsWsi7Kfl6icgJonA0cpYfTWKRj8IdLlOSo3yePjV3Llv8yndya8+0OzfHq2VydiekT1zXiGtGq4VNdflrkwBLMvZ+skf9aP0rk14Qj2lCJ61OHM+tlTCf+MUWwE/KME1pt0uoo93bzU4ufGE57ypyd42l2ShYyIvsXwf6U0pyM6Me9O2BO0NkiJGQjQ+zOsPBufL7OUJxj1o8bKr7VYOdbTLZsRvwNXXd15TQXOWLgfeB0YW4bneySLxgT10xbd7u263cfRNp7Eu4sYYp2rlwh/h/Tb/Nj5snK0oxADeMbyLWt872PlGIW1FGHdvl6G2T6ulJ+VMjwVEtt9z8r00clyTYp4kJ5cLfuA+cePTMvnCUZyZ0v9eF9tC6bi5QnC3rE0R5RFM92f6B3YJT7Ku2SK7TmDmmWDGAWTIsowvSVssiLfOt5lamH0c7/L9StrstaQ4qRshlc1pCU348pWnOlTGBW8/x9SavJr/VsoVc9nzHNxZGzlr+H1l/DbyO3eQ6j0y1ZhZs0B5iCfbIa4ZZoqUcYr5slXmZmGlr22fKzc9L0clvOEl+zdbMx9nFjKns0a17rrIWpn4XGC4fGi0Adtums0WrRtBtL9EyMLdr6tDKUXxNu7QaUZyJl2SMzqGGAlG4sFUa1L1KVY3yDeivSWhVpdWC1uqcB7poPQfrX+uLq/r7Y3SN1i3ybHnlgHL/0aZUOyecyrfWRGlNAzje0fXVX/yG1IPcuWVCkzPc4ccXwqVOPymkh6W/1zpaSnbcWwdxbOtF9jI09pPpnS8gRrYmc1qVB3KAesZbflSNasEjXHJ8josx/h3wq9jvqY2a3t30nUcmfsPEmryrLiyOFMelfyrztLEWvO078GlFMONPedRdoNX/DSIExJpPg9yxzekO4y/FJAnu0XbKfy3aKT/HGjkTXSOq5+mOAjeGo1851d26ZEZux/Q56otbtW/f1kPklwRwlfmc50evQrjbSPup84flstDp6lys/1+lhtsDX6mNGfdzIwkZ5Zcyh+jKYC0vUjAtjQrg0G0UT+ZtJ3kRmPp0KpWx6G8rlTAPbmOcUL0n3QBHh8+6ueL25j4VxdJfodQnrUuMWiRJm41KdH3AtLWalzi/tQ9x6vnY3SpydqGqnMNTd3cLab7aQMVm/REk5G+7tyn5YilLkLAxT6Cm+0VsVH7o0v4SCvyPliw4Nx5DcYQv823W1obbewW2IV7rOGc2IWtAW9Bdi744eZ7lHvY5eOdRd+iEcwnkMQdeS9EPaSZvKzpRlyV3q4fRPyApkKhaltz2bj8HlIo9kmVOT8QzJssmjGSrzXZymYzEcQkZS5hLOh881pFEcKfOdpmZjMNTlEZQ5NOFh7jGEvXPbuzkvl1O9vpa5hPLgXcCcuBgcnvxVxyq2X4iFypw38u45oHU4qqFudov/dRyGj+XUnFcot5y+a/Yi4K1zv1hnZNEfbr5mLLeQ2VzNMZxnWozOekt+fuz3RY3eVOqM5t3TR3/UzgHDa644DypLx3h3Fll5Q6nguYBPhlT9R/3jnPxthFcFjSo5mlAy5xTV1EwPmZr5xqVvdOazEJksnSqZytRsHNGiG7Ebakfdgp+NwgNsejuUv0vJfxHr//5sH1qPyHqYLDpnDg6pLabshz1F69OzvT9bJTHe5eW7vW1owbPwXWrFe773qD/e9W2Xxlb9DRJe63dVqvqliGTxdM+uqy6MoHzyxjkg8z3fiO7ScxaLb56NAs4Wzf2pRYnm9Il8s6Bbie86UvZork70WT2eHOAN+06RH4rUp9TW0XYe91yJ814l570Fzjlpp8zhtfNZ/d2sKi4bDpd+kTs71v1SirPteV59bnSzkgvfQa/HD2rwA0fKFmn/JUXCmarP5s1qaM60TO4J61iZTCTrAePMTvG+6yPb4xpexwHjv1OJvuNIug2ydCn/HdEJW0b0Eq2bLZKebzrWZ1Jv10irv0dJ/7vBF/Qv4srnN3Tli+vF/25wsHbt+u+vffZgbeWrm/r/OfhA/Ur9Rl2BNf65+gqo7al94HCi/qr+pv6+vr8+X//T+p+563vnNOaXqvRv/S//BSovqBc=</latexit> under-determined <latexit sha1_base64="nCIFL0QNopmQRSBhYa6iV/R4B74=">AABBynictVzbchu5EYU3t7Vz200e8zKJ1ilvynEkrSubra1UrSzJsta0LZuU7PXSdvEyommPOPQMKV+4essn5DX5lXxH/iB5yi+kL8AAQ2KmMYpjlCQMiNPd6AEa3Q3Q/Wkyzmfr6/+88MH3vv+DH/7ow4uXfvyTn/7s5x99/IujPJ1ng/hwkCZp9qjfy+NkPIkPZ+NZEj+aZnHvpJ/ED/svt/Hzh6dxlo/TSWf2dho/OemNJuPj8aA3g6bHWTyaJ71s/C5+9tHa+rV1+hetVjZ0ZU3pfwfpx9Gh6qqhStVAzdWJitVEzaCeqJ7KoXyrNtS6mkLbE7WAtgxqY/o8VmfqEmDn0CuGHj1ofQm/R/D0rW6dwDPSzAk9AC4J/GSAjNRlwKTQL4M6covo8zlRxtYq2guiibK9hb99TesEWmfqObRKONMzFIdjmalj9ScawxjGNKUWHN1AU5mTVlDyyBnVDChMoQ3rQ/g8g/qAkEbPEWFyGjvqtkef/4t6Yis+D3Tfufo3SXkZSqTaevRpQaGnTol+RG9zDp+xPAlwHgGFWI8Ra69J1yc0+gn0X0D7XShnVDM66UNZUOtZLXIbig+5LSL3oPiQeyKyBcWHbInIAyg+5IFGIjYjnfvxbSg+fFvkfB+KD3lfRD6A4kM+EJFHUHzIIxH5GIoP+VhE3oTiQ94Ukbeh+JC3RWQHig/ZEZGHUHzIQxG5C8WH3NXI6pWaQUmJzlhYlVtQL/NAS5FAy5Yo3w2yjj7sjYA1PajAyqt6B/76sTsBOo0rsLsB8+64AivPvD2wkX6sbItu0W7iw94SsfswA/zYfRH7tXpRgf06YKW9rMDKa60F/fxY2fregSc/9o6IvQs1P1beo+5Bix97L2DHmFZgD0TsffWqAhti9bMKrGz322BX/Fh5n+pAfz82xJrOK7CyPT0CD8aPlXerh9Dqxz4UsY/UmwrsIxH7DVh3P/abgB32XQXW7LGXaAcZkT8Sw4qto9YrViXWpkCtJ/BPir0lId+4D+0SZlRgRoQ5ERF7BWIvENEqEK1gufLCjubk78pc2gWiHYjoF3sT1mZi/2HRH2tJAGKnQOwsIeo8UnzXZiyn5F2YFgk5K3YurIWMKS3sN9ZiPR/qLa9B3CsheG4/p5l/laIljKBQU3XUnhd7PCMjeq5DvKbozYzS8JBxs8IquKg3IqrvQfVF1FsP6q2ImntQcxF16kGdiii78l1cN2AGWP3ju1jQE88A9pGrSwRewRbsOrdgjUYwfw7AC3xALffgb5tib6nUSYbRPO6TmOV4UrLEGdQWag3abVS4Q/F1QissBsm45z0d4+MT5jYWes2xFT4rdvKoyJiE0xmTPKOCDnqLEa2nZnRuU8sZeXdca4a/Vax7U2uG3yWNn5EXz7Vm+JmWfnYO2Tsa2zkHtg2raaq1b+tNaXD+hWmY+iXaddHi4ls90XMG6b1pSH9fv5n9c7yXbaqxfmy9GY3cGV9eGl8TGlbPuaPnZlTQe2Kv19SixiOZ6LjX1pvKkNIuOtFy2Kembwb7DPWbMfVmNA7A49qmmHvh1JvO3mkxGltvRuNIcd7zjDx5U29GY0TPrA9bb0YDsy09HefbelPLjhrg2NnWm1r1CWWBMQfEc55brFeUkZ8019TG5B/UZ2tcn391H8OczdMiRqinZH3bajr9Yi+rl8j4CzFYtVlDOdC/mDs+WJnGQm2K8RXLMCvt76t07B6Pmm+BFiNY/XwGIOXME5DQ5CTQeidAcUOMusojM7hNEYez5HgJ1dWtM9FbtHw5a1Rue0atUlxmR2v12CV7ndPcm5JP2CLNSnpoVb7hKoqShlolDcn0mujunV6vZe2vi7jpEmJazLQBnQjxSVp9nOrTetvR8WV9yjODwmc+dv5itvlYWxuMeVKyRShLHU+3n8kjuW24r15VNsfNn0X0RtFenZLVGNOJVC5GoSZbzN74gp4t7UM6k0MeTGMA7zHSVKaKT80wi4759IgsqmtvJd6oL5Oh43pOVtfY43r0yEGPPOjmMc427Bh3odaBmOEQnjoBUc6lQlcpaTxTvy9OR1N6g/URfVKykIYG25u4ZCHrouznJSqvAY2zgaP0cBrLdAy+u0JJjvp98tjYtWz5L9PJrTnf7tEcr57N1ZmYIXHdJK4RrRo+1eWnZQ4swcL7ySb5r/WjRH5NOKINlbg+dTizXiZ04h9TBDslzzih1SatjnJvNz+1/InhdKDM2TmeZqdkISOyfxHsTynNyYh+3LsD5gSdLUJCNjLE7owL78bn64zFOWb9uLHiWw12vsVky+bE39B1V1dOc5EjBt4HzpbmttFJi3zBmLhm2rrbtV2/+yDS3pNwZwlTtHPlCvH/lH6bHzNP1lZmBGoY30CubZ3vfaQUs6COerTL19sg09eV8pNChqdaarv/WZk+KUm2QxEXyoO79RA4D+iZeeEsyUjufKUP76N12VykPF3SI472mKJ4tvsjvQOj3Fdpl1yjNdelWTKCWTArogjTV8oiL/Ot51WmHkY7/79Qt7ouaw0pRspmcFlDUn4/pmjNlTKBWc3z9yWtJr/Ws6Ve9XwmNBdPnLX8HbT+Gn4buc1zGJ1+ySrcoDnAFOyT1Qi3RCs9wnjdKPEyM9PQss+Wn52Tppfbcp74mq2bjbFPG1M5oFnzRmctTP08NF44NF4E6rBDZ41Wi6bdWKJnYmzR0aeVofyacOs0oDwXKcsemUGNA6R0Y6kwqkORqhzjG9Q7kda6SKsHq9U9DXDXfAjSv9aXV/d3xe4eqZvk2wzIA+P4ZUirdEw+l2mtj9SYAnK+ru2ru/q71ILc+2RBkTLf48QVw6dOAypnhaS/1TtbSnbeWgRzb+m17mNsbJfqn60gT2hN5LQuDeI69Yi1/K4c0ZJFuub4HBFl/nvkU7HfUR8zu73tO4lK/oSNN3lVWV4cKUxI/1LmbX8let134teIYsK59q77QKv5G0YKjDGZBL9nmdMbwl2OTxLYo+2T/Vy1U3yKN3EkukZSL9SfA2wMR712rrtzy4zYjO130BO1bt+6r4fMLwnmKPE7z4lej3a1E+2jLpaez0erp3e58nOdHuZLfK0+5tTHjSxslFfGdNWXwVxYomZcGBPCpdkomsjfTPImMvPpVChl09tQLmca2MY8p3hJugeKCJ93d8XrzX0qjKO/Qq9PWJcat0iUMBuX6vyAa2kxK3VxZR/i1ou1u1Hi7ERVO4Wh7u4W1n6zhYzJ+iVKytlwb1f2bilKkbMwTGGg+EZvVXzo0vwSCv6OlC86NBxDcodt8G+31LbafQ+3IV7pOmc0I2pBWzBcir17epzlHvU6euVQd+mHcAjnMQZdS9KPaSdtKjtTliV3qYfTf01WIFOxKL3t2XwMLhd5JKucmoxnTJZNHs1Yme/iNB2L4RAykjKXcD58riGN4liZ7zQ1G4OhLo+gzKEJD3OPIeyd297Nebmc6vW1yiWUB+8C5sTF4PDkrzpWsf1CLFTmvJH3zwGtw3ENdbNb/K/jMHwsp+a8Qrnl9F2zFwFvnfvFOiOL/nDzNWO5hczmao7hPNNidNZb8vNjvy9q9KZSZzTvnz76o3YOGF4LxXlQWTrGu7PIyhtKBc8FfDKk6j/qHxfkbyO8KmhUydGEkjmnqKZmesjUzDcufaMzn4XIZOlUyVSmZuOINt2I3Vb76ib8bBceYNPbofxdSv6LWP/3Z4fQekzWw2TROXPQpbaYsh/2FG1Iz/b+bJXEeJeX7/Z2oAXPwlvUivd871J/vOvbKY2t+hskvNbvqFQNSxHJ8umeXVd9GEH55I1zQOZ7vhHdpecsFt88Owk4WzT3p5YlWtAn8s2CfiW+70g5oLk61Wf1eHKAN+x7RX4oUn+gtp6287jnSpwPKjkfLHHOSTtlDm+cz+rvZlVx2Xa4DIvc2anul1Kcbc/z6nOjO5Vc+A56PX5Ugx85UrZJ+y8pEs5UfTZvXkNzrmVyT1gnymQiWQ8YZ/aK910f2Z7W8DoNGP/tSvRtR9I9kKVP+e+ITtgyopdo3eyS9HzTsT6TeqtGWv09SvrfDb6gfxFXPr+uK19sFP+7wdHmtY0/Xvvs/ubaVzf0/3PwofqV+o26Amv8c/UVUDtQh8Bhov6q/qb+vtXayrbebi246wcXNOaXqvRv6y//BV5jpU4=</latexit> regularize <latexit 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Spike deconvolution: <latexit 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Ax = a ? x <latexit 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x0 <latexit 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y = x ? a + " <latexit 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x <latexit 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<latexit sha1_base64="DvsYbo9hB8zeOFMxhW8tXI1kFTY=">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</latexit> Data (ai, yi)n i=1 <latexit sha1_base64="YHdOt0d069yYdxf084ppd3pbpyY=">AABB0nictVxbdxu3EYbTW+zenPaxL9sq7nF6HFdWfJqmOT0nsiTLimmbNinZSWj78LKiaa+4NJekL4weevran9DX9m/0d/QftE/9C50LsMCS2B2s6hpHEhbENzOYBQYzA9C9STLKZpub/zz33ne++73v/+D98xd++KMf/+SnFz/42VGWzqf9+LCfJun0Ua+bxcloHB/ORrMkfjSZxt2TXhI/7L3Ywc8fLuJpNkrH7dmbSfz4pDscj45H/e4Mmp5evHgnHcRJBATiPrb84enFjc2rm/QvWq9c05UNpf810w+iQ9VRA5WqvpqrExWrsZpBPVFdlUH5Rl1Tm2oCbY/VEtqmUBvR57E6VRcAO4deMfToQusL+D2Ep2906xiekWZG6D5wSeBnCshIXQJMCv2mUEduEX0+J8rYWkZ7STRRtjfwt6dpnUDrTD2DVglneobicCwzdax+T2MYwZgm1IKj62sqc9IKSh45o5oBhQm0YX0An0+h3iek0XNEmIzGjrrt0uf/op7Yis993Xeu/k1SXoISqZYefZpT6KoF0Y/obc7hM5YnAc5DoBDrMWLtFen6hEY/hv5LaL8L5ZRqRic9KEtqPa1E7kDxIXdE5D4UH3JfRDag+JANEdmE4kM2NRKxU9K5H9+C4sO3RM73ofiQ90XkAyg+5AMReQTFhzwSkV9D8SG/FpE3ofiQN0XkbSg+5G0R2YbiQ7ZF5CEUH/JQRO5B8SH3NLJ8pU6hpERnJKzKbagXeaClSKBlW5TvBllHH/ZGwJrul2DlVb0Lf/3Y3QCdxiXYvYB5d1yClWfePthIP1a2RbdoN/Fhb4nYA5gBfuyBiP1SPS/Bfhmw0l6UYOW11oB+fqxsfe/Akx97R8TehZofK+9R96DFj70XsGNMSrBNEXtfvSzBhlj9aQlWtvstsCt+rLxPtaG/HxtiTeclWNmeHoEH48fKu9VDaPVjH4rYR+p1CfaRiP0KrLsf+1XADvu2BGv22Au0gwzJH4lhxVZR6+arEmsToNYV+Cf53pKQb9yDdgkzzDFDwpyIiP0csR+IaOSIRrBcWW5HM/J3ZS6tHNEKRPTyvQlrM7H/IO+PtSQAsZsjdlcQVR4pvmszlgV5F6ZFQs7ynQtrIWNKc/uNtVjPh2rLaxD3Cgie289o5l+haAkjKNRUFbVn+R7PyIieqxCvKHozozQ8ZNwstwou6rWI6nlQPRH1xoN6I6LmHtRcRC08qIWIsivfxXUCZoDVP76LJT3xDGAfubxE4BVsw65zC9ZoBPOnCV7gA2q5B39bFHtLpUoyjOZxn8Qsx+OCJZ5Cbak2oN1GhbsUXye0wmKQjHve0zE+PmFuY6nXHFvh03wnj/KMSTidEckzzOmgtxjReqpH5za1nJJ3x7V6+Fv5uje1evg90vgpefFcq4efaelnZ5C9rbHtM2BbsJomWvu2XpcG51+YhqlfoF0XLS6+1RM9Z5De65r0D/SbOTjDe9mhGuvH1uvRyJzxZYXx1aFh9Zw5eq5HBb0n9npNLao9krGOe229rgwp7aJjLYd9qvtmsM9AvxlTr0ejCR7XDsXcS6ded/ZO8tHYej0aR4rznqfkyZt6PRpDemZ92Ho9Gpht6eo439brWnbUAMfOtl7Xqo8pC4w5IJ7z3GK9oin5SXNNbUT+QXW2xvX51/cxzNk8yWOEakrWty2n08v3smqJjL8Qg1Wb1ZQD/Yu544MVaSzVlhhfsQyzwv6+Tsfu8aj5BmgxgtXPZwBSzjwBCU1OAq13AhSviVFXcWQGtyXicJYcr6A6unUmeouWL2eNim1PqVWKy+xorR47ZK8zmnsT8gkbpFlJD43SN1xGUdJQo6AhmV4d3b3V67Wo/U0RN1lBTPKZ1qcTIT5Jq45TfVpvOTq+pE95ZlD4zMfOX8w2H2trgzFPSrYIZani6fYzeSS3DffVK8rmuPmziN4o2qsFWY0RnUhlYhRqssXsjS/p2dI+pDM55ME0+vAeI01lovjUDLPomE+PyKK69lbijfoyGTquZ2R1jT2uRg8d9NCDrh/j7MCOcRdqbYgZDuGpHRDlXMh1lZLGp+rj/HQ0pTdYHdEnBQtpaLC9iQsWsirKflag8grQOBs4Sg+nsUrH4DtrlOSo3yePjV2Llv8Sndya8+0uzfHy2VyeiRkQ1y3iGtGq4VNdflrlwBIsvZ9skf9aPUrkV4cj2lCJ6xOHM+tlTCf+MUWwE/KME1pt0uoo9nbzU6ufGE5NZc7O8TQ7JQsZkf2LYH9KaU5G9OPeHTAn6GwRErKRIXZnlHs3Pl9nJM4x68eNFN9qsPMtJls2J/6Grru6MpqLHDHwPnC6MreNThrkC8bEdaqtu13b1bsPIu09CXeWMEU7Vy4T/4/ot/kx82RjbUaghvENZNrW+d5HSjEL6qhLu3y1DTJ9XSk/zGV4oqW2+5+V6cOCZLsUcaE8uFsPgHOfnpkXzpIpyZ2t9eF9tCqbi5QnK3rE0R5TFM92f6h3YJT7Cu2SG7TmOjRLhjALZnkUYfpKWeRVvtW8itTDaGf/F+pW10WtIcVI2Qwua0jK78cUrblSJjCref6+oNXk1/p0pVc1nzHNxRNnLX8Lrb+E30Zu8xxGp1ewCjdoDjAF+2Q1wi3RWo8wXjcKvMzMNLTss+Vn56Tp5bacJb5m62Zj7EVtKk2aNa911sLUz0LjuUPjeaAO23TWaLVo2o0leirGFm19WhnKrw63dg3Kc5Gy7JEZ1ChASjeWCqM6EKnKMb5BvRVpbYq0urBa3dMAd82HIP1rfXV1f5vv7pG6Sb5Nnzwwjl8GtEpH5HOZ1upIjSkg5+vavrqrv0MtyL1HFhQp8z1OXDF86tSncppL+mu9s6Vk561FMPeWXuk+xsZ2qP7JGvKE1kRG69IgrlOPWMvvyhGtWKSrjs8RUea/Sz4V+x3VMbPb276TqOBP2HiTV5XlxZHCmPQvZd4O1qLXAyd+jSgmnGvvuge06r9hpMAYk0nwe5YZvSHc5fgkgT3aHtnPdTvFp3hjR6KrJPVS/THAxnDUa+e6O7fMiM3YfgM9Uev2rft6yPySYI4Sv7Oc6HVpVzvRPupy5flstLp6lys+V+lhvsLX6mNOfdzIwkZ5RUxHfR7MhSWqx4UxIVzqjaKO/PUkryMzn06FUja9DeVipoFtzDOKl6R7oIjweXeXvd7cR8I4emv0eoR1qXGLRAmzcanOD7iWFrNS59f2IW49X7kbJc5OVLZTGOrubmHtN1vImKxfoqScDfd2Ze8UohQ5C8MU+opv9JbFhy7Nz6Hg70j5okPDMSR32AL/dlvtqL13cBvipa5zRjOiFrQFg5XYu6vHWexRraOXDnWXfgiHcB4j0LUk/Yh20rqyM2VZcpd6OP1XZAWmKhaltz3rj8HlIo9knVOd8YzIssmjGSnzXZy6YzEcQkZS5BLOh881pFEcK/OdpnpjMNTlERQ51OFh7jGEvXPbuz4vl1O1vta5hPLgXcCcuBgcnvyVxyq2X4iFmjpv5N1zQOtwXEHd7Bb/6zgMH8upPq9Qbhl91+x5wFvnfrHOyKI/XH/NWG4hs7mcYzjPNB+d9Zb8/Njvi2q9qdQZzbunj/6onQOG11JxHlSWjvHuLLLyhlLBcwGfDKn6j/rHOfnbCC9zGmVy1KFkzinKqZkeMjXzjUvf6MxnITJZOmUyFanZOKJFN2J31IG6CT87uQdY93Yof5eS/yLW//3ZAbQek/UwWXTOHHSoLabshz1FG9CzvT9bJjHe5eW7vW1owbPwBrXiPd+71B/v+rYLYyv/Bgmv9TsqVYNCRLJ6umfXVQ9GUDx54xyQ+Z5vRHfpOYvFN89OAs4Wzf2pVYmW9Il8s6BXiu85UvZprk70WT2eHOAN+26eH4rUb6mtq+087rkS52Yp5+YK54y0U+Tw2vms+m5WGZcdh8sgz50tdL+U4mx7nledG90t5cJ30Kvxwwr80JGyRdp/QZHwVFVn8+YVNOdaJveEdaxMJpL1gHFmN3/f1ZHtooLXImD8t0vRtx1J90GWHuW/IzphmxK9ROtmj6Tnm47VmdRbFdLq71HS/27wGf2LuPLpdV357Fr+vxscbV299rurn9zf2vjihv5/Dt5Xv1C/UpdhjX+qvgBqTXUIHBbqr+pv6u/b7e2323/a/jN3fe+cxvxcFf5t/+W/Ulenkg==</latexit> Model selection: <latexit 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yi ⇡ hai, xi <latexit 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Lasso: ||x||1 <latexit 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Ridge: ||x||2 2
  6. 2⌧ 2 Forward-Backward splitting • ˆ k+1 = k ⌧X>

    rLy (X k ) • k+1 = ˆ k+1 ⌧rR (ˆ k+1 ) and its siblings: FISTA, FISTA with restarts, variab metric/quasi-Newton proximal methods. Forward-Backward <latexit sha1_base64="iaP8TP8Hzy0Jg9H0z5MLH35sX2Y=">AABCEXictVxfcxu3EYfTf7H7z2kf+4JWccdubVdSPE0zmcyElmRZMW3RJiU7CW3NkTzRtI48+u4oS2b4KfpZ+tCndvraT9DpazvTPvUrdHcBHHAk7oBTXWMk4UD8dhd7wGJ3Abo3jUZptr7+t0vvfevb3/nu996/fOX7P/jhj3589YOfHKbxLOmHB/04ipNnvSANo9EkPMhGWRQ+myZhMO5F4dPeyRZ+/vQ0TNJRPOlk59Pw+TgYTkbHo36QQdPR1f2zo/nJrzcW/DPezcKzbN5K4rPF0bybBTPejYDQIODdSZyM593+IM4WRxuL6/yc3+LUo/Gim8VTfr1xdnRy6/wGv3F0dW399jr946uVDVlZY/JfK/6AH7AuG7CY9dmMjVnIJiyDesQClkL5mm2wdTaFtudsDm0J1Eb0ecgW7ApgZ9ArhB4BtJ7A7yE8fS1bJ/CMNFNC94FLBD8JIDm7BpgY+iVQR26cPp8RZWwtoz0nmijbOfztSVpjaM3YS2h14VRPXxyOJWPH7Hc0hhGMaUotOLq+pDIjraDk3BhVBhSm0Ib1AXyeQL1PSKVnTpiUxo66Dejzf1FPbMXnvuw7Y/8mKa9B4awtRx/nFAJ2SvQ5vc0ZfCbkiYDzECiEcoxYe0O6HtPoJ9B/Du2PoCyopnTSgzKn1kUlcguKDbnlRO5CsSF3ncgmFBuy6US2oNiQLYlEbEI6t+PbUGz4tpPzYyg25GMn8gkUG/KJE3kIxYY8dCK/gmJDfuVE3oNiQ95zIh9AsSEfOJEdKDZkx4k8gGJDHjiRO1BsyB2JLF+pCZSY6Iwcq7IB9SIPtBQRtDSc8t0l62jD3vVY0/0SrHtVb8NfO3bbQ6dhCXbHY94dl2DdM28XbKQd67ZF92k3sWHvO7F7MAPs2D0n9gv2qgT7hcdKOynButdaE/rZsW7r+xCe7NiHTuwjqNmx7j1qH1rs2H2PHWNagm05sY/Z6xKsj9VPSrBuu98Gu2LHuvepDvS3Y32s6awE67anh+DB2LHu3eoptNqxT53YZ+ysBPvMif0SrLsd+6XHDvu2BKv22Cu0gwzJHwlhxVZRC/JVibUpUAsc/KN8b4nIN+5BuwszzDFDwoydiN0cseuJaOaIprdcaW5HU/J33VzaOaLtiejlexPWMmf/Qd4fa5EHYjtHbC8hqjxSfNdqLKfkXagWFzLLdy6s+Ywpzu031kI5H6otr0LsFxBibr+kmX+ToiWMoFBTVdRe5nu8QHJ6rkK8oehNjVLxcOOy3CqYqDMnqmdB9Zyocwvq3ImaWVAzJ+rUgjp1ovTKN3Fdjxmg9Y/vYk5PYgYIH7m8cPAKGrDr3Ic1ymH+tMALfEIt+/C3TbG3q1RJhtE87pOY5XhesMQJ1OZsDdp1VLhN8XVEKywEyUTPfRnj4xPmNuZyzQkrvMh3cp5nTPzpjEieYU4HvUVO66kenQfUsiDvTtTq4e/n617V6uF3SOML8uJFrR4+k9JnF5C9I7GdC2DbsJqmUvu6XpeGyL8IGqp+hXZdtLj4VsdyziC9s5r09+Sb2bvAe9mimtCPrtejkRrjSwvjq0ND6zk19FyPCnpPwutVNV57JBMZ9+p6XRli2kUnUg79VPfNYJ+BfDOqXo9GCzyuLYq550a97uyd5qPR9Xo0DpnIey7Ik1f1ejSG9Cz0oev1aGC2JZBxvq7XteyoARE763pdqz6hLDDmgMScFy3aK0rIT5pJaiPyD6qzNabPv7qPYc7mRR4jVFPSvm05nV6+l1VLpPyFEKxaVlMO9C9mhg9WpDFnm874SsiQFfb3VTp6j0fNN0GLHFa/OANw5cwjkFDlJNB6R0Bxwxl1FUemcJtOHM6S4yVUV7ZmTm9R8xVZo2LbEbW64jI9Wq3HLtnrlObelHzCJmnWpYdm6Rsuo+jSULOgITe9Orp7K9drUfvrTtx0CTHNZ1qfToTESVp1nGrTetvQ8TV5ypNBEWc+ev5itvlYWhuMeWKyRShLFU+zn8ojmW24r95kOsctPuP0RtFenZLVGNGJVOqMQlW2WHjjc3rWtA/oTA55CBp9eI9cUpkycWqGWXTMp3OyqKa9dfFGfakMnainZHWVPa5GDw300IKuH+NswY7xCGodiBkO4KnjEeVcyXUVk8YTdis/HY3pDVZH9FHBQioawt6EBQtZFWW/LFB5A2icDSJK96exTEfhuyuU3FG/TR4duxYt/zU6uVXn2wHN8fLZXJ6JGRDXTeLKadWIU13xtMxBSDC3frJJ/mv1KJFfHY5oQ11cXxichV4mdOIfUgQ7Jc84otXmWh3F3mZ+avkTxanF1Nk5nmbHZCE52T8O+1NMc5LTj3l3QJ2gC4sQkY30sTuj3Lux+Toj5xzTftyIiVsNer6FZMtmxF/RNVdXSnNRRAxiH1gszW2lkyb5giFxTaR112u7evdBpL4nYc4SQVHPlevE/wb9Vj9qnqytzAjUML6BVNo62/uIKWZBHQW0y1fbINXXlPLDXIYXUmq9/2mZPixItk0RF8qDu/UAOPfpWfDCWZKQ3OlKH7GPVmVzkfJ0SY842mOK4oXdH8odGOW+SbvkGq25Ls2SIcyCLI8iVF9XFnmZbzWvInU/2un/hbrWdVFrSJEzncEVGnLl90OK1kwpI5jVYv6e0Gqyaz1Z6lXNZ0JzcWys5W+g9efwW8mtnv3o9ApW4S7NAUFBP2mNiBa+0sOP190CLzUzFS39rPnpOal6mS0Xia+FddMx9mltKi2aNWcya6HqF6HxyqDxylOHHTpr1FpU7coSHTlji448rfTlV4dbpwblmZOy2yNTqJGHlGYs5Ud14KTqjvEV6q2T1rqTVgCr1TwNMNe8D9K+1pdX9zf57s7ZPfJt+uSBifhlQKt0RD6Xaq2O1AQF5HxH2ldz9XepBbn3yIIiZXGPE1eMOHXqU1nkkv5S7mwx2XltEdS9pTeyj7KxXap/tIIc05pIaV0qxB3qEUr5TTn4kkW6bfgcnDL/AflUwu+ojpnN3vqd8II/oeNNsao0LxEpTEj/rszb3kr0umfEr5xiwpn0rntAq/4bRgoCozIJds8ypTeEu5w4SRAebY/s56qdEqd4E0Oi2yT1nH3mYWNE1Kvnujm31IjV2H4FPVHr+q3berj5Rd4cXfwucqIX0K42lj7qfOn5YrQCucsVn6v0MFviq/Uxoz5mZKGjvCKmyz715iIkqsdFYHy41BtFHfnrSV5HZnE65UtZ9VaUi5kGYWNeUrzkugeKCJt3d93qzd1wjKO3Qq9HWJOaaHFRwmxcLPMDpqXFrNTllX1ItF6u3I0iYycq2ykUdXO30PZbWMiQrF/EXDkb0duUvVuIUtxZGEGhz8SN3rL40KT5KRT8zZktOlQcfXKHbfBvG2yL7byD2xCvZV1kNDm1oC0YLMXegRxnsUe1jl4b1E36Phz8eYxA1y7pR7ST1pVdUHZLblL3p/+GrEDCQqf0umf9MZhc3CNZ5VRnPCOybO7RjJj6Lk7dsSgOPiMpcvHnI841XKM4Zuo7TfXGoKi7R1DkUIeHusfg98517/q8TE7V+lrl4stD7ALqxEXh8OSvPFbR/XwsVGK8kXfPAa3DcQV1tVv8r+NQfDSn+rx8uaX0XbNXHm9d9AtlRhb94fprRnPzmc3lHP15xvnotLdk5yf8Pl7rTcXGaN49ffRH9RxQvOZM5EHd0gm8OYu0vL5U8FzAJkPM/sP+dMn9bYTXOY0yOepQUucU5dRUDzc19Y1L2+jUZz4yaTplMhWp6TiiTTdit9geuwc/W7kHWPd2qPgupfiLWPv3ZwfQekzWQ2XRReagS20hZT/0KdqAnvX92TKJ8S6vuNvbgRY8C29SK97zfUT98a5vpzC28m+QiLX+kMVsUIhIlk/39LrqwQiKJ28iB6S+58vpLr3IYombZ2OPs0V1f2pZojl94r5Z0CvF9wwp+zRXp/KsHk8O8IZ9kOeHOPsNtQXSzuOe6+LcKuXcWuKcknaKHM6Mz6rvZpVx2TK4DPLc2ansF1Ocrc/zqnOj26VcxB30avywAj80pGyT9k8oEk5YdTZvVkFzJmUyT1gnTGUihR4wzgzy910d2Z5W8Dr1GP+DUvQDQ9JdkKVH+W9OJ2wJ0YukbnZIenHTsTqTer9CWvk9SvrfDT6hf1xUPr4jK59s5P+7weHm7Y3f3v7o8Z21z+/K/+fgffYz9gt2Hdb4x+xzoNZiB8DhD+zv7B/sn43fN/7Y+HPjL6Lre5ck5qes8K/x1/8CZxq/kw==</latexit> xk+1 = Prox⌧ ||·||1 (y ⌧A>(Axk y)) <latexit sha1_base64="F951Nm+rra9ve6UDYp3LMnIQF58=">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</latexit> Prox ||·||1 (x) = (sign(xi)(|xi | )+)i <latexit 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⌧ < 2 kAk <latexit 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k <latexit 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min x2Rd f(x) , 1 2 kAx yk2 + kxk1 <latexit 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x <latexit 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<latexit 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Prox ||·||1
  7. 2⌧ 2 Forward-Backward splitting • ˆ k+1 = k ⌧X>

    rLy (X k ) • k+1 = ˆ k+1 ⌧rR (ˆ k+1 ) and its siblings: FISTA, FISTA with restarts, variab metric/quasi-Newton proximal methods. Forward-Backward <latexit sha1_base64="iaP8TP8Hzy0Jg9H0z5MLH35sX2Y=">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</latexit> xk+1 = Prox⌧ ||·||1 (y ⌧A>(Axk y)) <latexit sha1_base64="F951Nm+rra9ve6UDYp3LMnIQF58=">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</latexit> Prox ||·||1 (x) = (sign(xi)(|xi | )+)i <latexit 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⌧ < 2 kAk <latexit 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k <latexit 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min x2Rd f(x) , 1 2 kAx yk2 + kxk1 <latexit 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x <latexit 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Prox ||·||1 <latexit 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f(xk) min f 6 Cn,d k <latexit sha1_base64="rD2uViTq2LCt//2OHuuLL1eGPaA=">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</latexit> Theorem: <latexit sha1_base64="VltScW0qieg47mBCbdXDqVZez6c=">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</latexit> Nesterov, FISTA accelerations: 1/k2 rates.
  8. 2⌧ 2 Forward-Backward splitting • ˆ k+1 = k ⌧X>

    rLy (X k ) • k+1 = ˆ k+1 ⌧rR (ˆ k+1 ) and its siblings: FISTA, FISTA with restarts, variab metric/quasi-Newton proximal methods. Forward-Backward <latexit sha1_base64="iaP8TP8Hzy0Jg9H0z5MLH35sX2Y=">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</latexit> xk+1 = Prox⌧ ||·||1 (y ⌧A>(Axk y)) <latexit sha1_base64="F951Nm+rra9ve6UDYp3LMnIQF58=">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</latexit> Prox ||·||1 (x) = (sign(xi)(|xi | )+)i <latexit 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⌧ < 2 kAk <latexit 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k <latexit 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min x2Rd f(x) , 1 2 kAx yk2 + kxk1 <latexit 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x <latexit 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Prox ||·||1 <latexit 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f(xk) min f 6 C k 4 4+dim <latexit 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(deconvolution + min-separation) <latexit 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Grid-free rates [L´ eger, Chizat]: <latexit sha1_base64="oORH+79GGWu2NX9Kh4QXoFA0ncM=">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</latexit> f(xk) min f 6 Cn,d k <latexit sha1_base64="rD2uViTq2LCt//2OHuuLL1eGPaA=">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</latexit> Theorem: <latexit sha1_base64="VltScW0qieg47mBCbdXDqVZez6c=">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</latexit> Nesterov, FISTA accelerations: 1/k2 rates.
  9. 1 2 2 Quadratic variational formulation: k k1 = inf⌘>0

    1 2 P i ⌘ 1 i | i | 2 + 1 2 P i ⌘ i . 7 / 49 <latexit 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“⌘-trick” Iterative Reweighted Least Squares <latexit 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|x| = inf ⌘>0 1 2 x2 ⌘ + 1 2 ⌘ <latexit 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⌘? = |x|
  10. 1 2 2 Quadratic variational formulation: k k1 = inf⌘>0

    1 2 P i ⌘ 1 i | i | 2 + 1 2 P i ⌘ i . 7 / 49 <latexit 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“⌘-trick” Iterative Reweighted Least Squares <latexit sha1_base64="snzG/SUNhxJOSDZedYIkBqAlzNM=">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</latexit> |x| = inf ⌘>0 1 2 x2 ⌘ + 1 2 ⌘ <latexit sha1_base64="SaxMCG/AIDgBrgxMVRkSten/UyU=">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</latexit> min x2Rd 1 2 kAx yk2 + kxk1 <latexit sha1_base64="lLsRnvUWJkY/RQ0TaBM4L4cAAjc=">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</latexit> Jointly convex <latexit 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over <latexit 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parameterization <latexit 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min x2Rd,⌘2Rd + 1 2 ||Ax y||2 + 1 2 X i x2 i ⌘i + ⌘i <latexit 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⌘? = |x|
  11. 1 2 2 Quadratic variational formulation: k k1 = inf⌘>0

    1 2 P i ⌘ 1 i | i | 2 + 1 2 P i ⌘ i . 7 / 49 <latexit 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“⌘-trick” Iterative Reweighted Least Squares <latexit sha1_base64="snzG/SUNhxJOSDZedYIkBqAlzNM=">AABDEHictVxbdxu3EYbTW+zenPaxL9sq7nFaV5UUp0lOTnpiXSwrlm3apGQnpu3Dy4qmTXFpLinLpvkn+jv6A/qW09c+9i2n/QHtU/9C5wIssCR2B6u62kMJi8U3M5gFBjMDUO3RoJ9O1ta+PffOd777ve//4N3zF374ox//5KcX3/vZYZpMx534oJMMkvGDdiuNB/1hfDDpTwbxg9E4bh23B/H99vMtfH7/JB6n/WTYmLwaxY+OW71h/6jfaU2g6snF629O30SfR83+8OjJrNmJJ60/rs2j5tG41Zmtz2cbpnz6eGPOz+fRb/PPsfLJxZW11TX6iZYL67qwovRPLXkv+lY1VVclqqOm6ljFaqgmUB6olkrheqjW1ZoaQd0jNYO6MZT69DxWc3UBsFNoFUOLFtQ+h989uHuoa4dwjzRTQneAywA+Y0BG6hJgEmg3hjJyi+j5lChjbRHtGdFE2V7B37amdQy1E/UUaiWcaRmKw75M1JH6hPrQhz6NqAZ719FUpqQVlDxyejUBCiOow3IXno+h3CGk0XNEmJT6jrpt0fN/UUusxfuObjtV/yYpL8EVqbrufZJRaKkToh/R25zCM5ZnAJx7QCHWfcTSS9L1MfV+CO1nUH8brjmVjE7acM2odl6K3ILLh9wSkbtw+ZC7InIfLh9yX0TW4PIhaxqJ2DHp3I+vw+XD10XOd+HyIe+KyHtw+ZD3ROQhXD7koYj8Gi4f8msReR0uH/K6iLwJlw95U0Q24PIhGyLyAC4f8kBE7sDlQ+5oZPFMHcOVEJ2+MCuvQTnPAy3FAGquifJtknX0YTcD5nSnACvP6m3468duB+g0LsDuBIy7owKsPPJ2wUb6sbItukGriQ97Q8TuwQjwY/dE7JfqWQH2y4CZ9rwAK8+1fWjnx8rW9xbc+bG3ROxtKPmx8hp1B2r82DsBK8aoAFsTsXfViwJsiNUfF2Blu18Hu+LHyutUA9r7sSHWdFqAle3pIXgwfqy8Wt2HWj/2voh9oE4LsA9E7Fdg3f3YrwJW2NcFWLPGXqAVpEf+SAwztoxaK5uVWBoBtZbAf5CtLQPyjdtQL2F6GaZHmGMRsZshdgMR+xliP1iuNLOjKfm7Mpd6hqgHItrZ2oSlidi+m7XH0iAAsZ0hthcQZR4pvmvTlxPyLkyNhJxkKxeWQvqUZPYbS7EeD+WW1yDu5BA8tp/SyL9C0RJGUKipMmpPszWekRHdlyFeUvRmeml4yLhJZhVc1KmIantQbRH1yoN6JaKmHtRURJ14UCciys58F9cMGAFW//guZnTHI4B95OIrAq/gGqw6N2CORjB+auAF3qOaO/C3TrG3dJVJhtE8rpOY5XiUs8RjKM3UCtTbqHCb4usBzbAYJOOWd3SMj3eY25jpOcdWeJ6t5FGWMQmn0yd5ehkd9BYjmk/V6Nykmjl5d1yqhr+RzXtTqobfIY3PyYvnUjX8REs/OYPsDY1tnAFbh9k00tq35ao0OP/CNEz5Aq26aHHxrR7rMYP0TivS39NvZu8M72WLSqwfW65GI3X6l+b6V4WG1XPq6LkaFfSe2Os1pahyT4Y67rXlqjIktIoOtRz2ruqbwTZd/WZMuRqNGnhcWxRzz5xy1dE7ynpjy9VoHCrOe87JkzflajR6dM/6sOVqNDDb0tJxvi1XteyoAY6dbbmqVR9SFhhzQDzmucZ6RWPyk6aaWp/8g/JsjevzL69jmLN5nMUI5ZSsb1tMp52tZeUSGX8hBqs2qSgH+hdTxwfL05ipDTG+YhkmufV9mY5d41Hz+6DFCGY/7wFIOfMBSGhyEmi9B0BxXYy68j0zuA0Rh6PkaAHV1LUT0Vu0fDlrlK97QrVSXGZ7a/XYJHud0tgbkU+4T5qV9LBf+IaLKEoa2s9pSKZXRXev9XzNa39NxI0WEKNspHVoR4h30srjVJ/W646OL+ldnglcvOdjxy9mm4+0tcGYJyFbhLKU8XTbmTySW4fr6hVlc9z8LKI3ivbqhKxGn3akUjEKNdli9sZndG9pH9CeHPJgGh14j5GmMlK8a4ZZdMynR2RRXXsr8UZ9mQwdl1OyusYel6N7DrrnQVePcbZgxbgNpQbEDAdw1wiIci5kukpI42P1u2x3NKE3WB7RD3IW0tBgexPnLGRZlP00R+UloHE0cJQeTmORjsE3lyjJUb9PHhu75i3/Jdq5NfvbLRrjxaO5OBPTJa4bxDWiWcO7uny3yIElmHmfbJD/Wt5L5FeFI9pQietjhzPrZUg7/jFFsCPyjAc026TZkW/t5qcWnxhONWX2znE3OyELGZH9i2B9SmhMRvRxzw6YHXS2CAOykSF2p595Nz5fpy+OMevH9RWfarDjLSZbNiX+hq47u1Iaixwx8DowXxjbRif75AvGxHWsrbud2+WrDyLtOQl3lDBFO1YuE/8P6Lf5mHGysjQiUMP4BlJt63zvI6GYBXXUolW+3AaZtq6U72cyPNZS2/XPyvR+TrJtirhQHlytu8C5Q/fMC0fJmOROl9rwOlqWzUXKowU9Ym+PKIpnu9/TKzDKfYVWyRWac00aJT0YBZMsijBtpSzyIt9yXnnqYbTT/wt1q+u81pBipGwGlzUk5fdjitZcKQcwqnn8PqfZ5Nf6eKFVOZ8hjcVjZy6/gdpfwm8jt7kPo9POWYVNGgNMwd5ZjXBNtNQijNdmjpcZmYaWvbf87Jg0rdyas8TXbN1sjH1SmUqNRs2pzlqY8lloPHNoPAvUYYP2Gq0WTb2xRE/E2KKhdytD+VXh1qhAeSpSlj0yg+oHSOnGUmFUuyJVOcY3qNcirTWRVgtmq7sb4M75EKR/ri/O7jfZ6h6p6+TbdMgD4/ilS7O0Tz6XqS2P1JgCcr6q7as7+5tUg9zbZEGRMp/jxBnDu04duuaZpL/WK1tCdt5aBHNu6aVuY2xsk8ofLiGPaU6kNC8N4iq1iLX8rhzRgkVadXyOiDL/LfKp2O8oj5nd1vadRDl/wsabPKssL44UhqR/KfO2txS97jnxa0Qx4VR7122gVf0NIwXGmEyC37NM6Q3hKsc7CezRtsl+Ltsp3sUbOhKtktQz9XmAjeGo1451d2yZHpu+/QZaotbtW/e1kPkNgjlK/M6yo9eiVe1Y+6izhfuz0WrpVS5/X6aH6QJfq48ptXEjCxvl5TFN9VkwF5aoGhfGhHCp1osq8leTvIrMvDsVStm0NpTzmQa2MU8pXpLOgSLC591d9npzHwj9aC/RaxPWpcY1EiXMxiU6P+BaWsxKnV9ah7j2fOlqNHBWoqKVwlB3Vwtrv9lCxmT9BkrK2XBrV/ZmLkqRszBMoaP4RG9RfOjS/Awu/B0pX3RoOIbkDuvg315TW2rnLZyGeKHLnNGMqAZtQXch9m7pfuZblOvohUPdpR/CIZxHH3QtSd+nlbSq7ExZltylHk7/JVmBsYpF6W3L6n1wucg9WeZUpT99smxyb/rKfBenal8Mh5Ce5LmE8+F9DakXR8p8p6laHwx1uQd5DlV4mHMMYe/ctq7Oy+VUrq9lLqE8eBUwOy4Ghzt/xbGKbRdiocbOG3n7HNA6HJVQN6vF/9oPw8dyqs4rlFtK3zV7FvDWuV2sM7LoD1efM5ZbyGgu5hjOM8l6Z70lPz/2+6JKbypxevP26aM/aseA4TVTnAeVpWO8O4qsvKFUcF/AJ0Oi/qO+OSd/G+FFRqNIjiqUzD5FMTXTQqZmvnHp6515FiKTpVMkU56ajSPqdCJ2S+2p6/DZyjzAqqdD+buU/Bex/u/PdqH2iKyHyaJz5qBJdTFlP+wuWpfu7fnZIonxLC+f7W1ADe6F71MtnvO9Te3xrG8j17fib5DwXL+lEtXNRSSLu3t2XrWhB/mdN84Bme/5RnSWnrNYfPLsOGBv0ZyfWpRoRk/kkwXtQnzbkbJDY3Wk9+px5wBP2Ley/FCkfk91LW3ncc2VONcKOdcWOKeknTyHU+dZ+dmsIi5bDpduljs70e0SirPtfl55bnS7kAufQS/H90rwPUfKOmn/OUXCY1WezZuW0Jxqmdwd1qEymUjWA8aZrex9l0e2JyW8TgL6f7MQfdORdBdkaVP+O6IdtjHRG2jd7JD0fNKxPJN6o0Ra8z1Kaezy9yE4L2H+18BDyku1yQqsqSv0WVWfQMtp0Ew8EWgirSua8lzrtTxjYs9XllH9KJP1I4UZJIMC6vRfHj6ln4gLH1/VhU/Xs//ycLixuv6H1Q/vXl35YlP/v4d31S/Ur9RlsHUfqy9AqzV1APz/rP6u/qH+ufmnzb9sfrP5V276zjmN+bnK/Wz+7b8mBe/N</latexit> |x| = inf ⌘>0 1 2 x2 ⌘ + 1 2 ⌘ <latexit sha1_base64="SaxMCG/AIDgBrgxMVRkSten/UyU=">AABB/3ictVzNc9u4FUe2X5v0K9see2HrTSfbZlPbm+l2Z2dn1rEdxxsnUSLZye4q8VASrTChRIWUHCeKDv1beuit02tPPffanvoftKf+C30fAAFKIAG6W2NsgSB+7z08Ag/vPVDuTZI4n66v//PCO9/69ne++713L176/g9++KMfX37vJ0d5Osv60WE/TdLscS/MoyQeR4fTeJpEjydZFI56SfSo92Ib7z86jbI8Tsed6etJ9GQUDsfxSdwPp9B0fPmz7igeH8/Pgm48DroPHz4dLILuSRb25xuL+WY3AUqDcNF9G2wFZ8GHr4Pu26ebwa/h46z79njj+PLa+vV1+glWKxuysibkTyt9LzgUXTEQqeiLmRiJSIzFFOqJCEUO5WuxIdbFBNqeiDm0ZVCL6X4kFuISYGfQK4IeIbS+gL9DuPpato7hGmnmhO4DlwR+M0AG4gpgUuiXQR25BXR/RpSxtYr2nGiibK/hsydpjaB1Kp5BqwunevricCxTcSJ+R2OIYUwTasHR9SWVGWkFJQ+MUU2BwgTasD6A+xnU+4RUeg4Ik9PYUbch3f8X9cRWvO7LvjPxb5LyCpRAtOXo04JCKE6JfkBPcwb3WJ4EOA+BQiTHiLVXpOsRjX4M/efQfg/KgmpKJz0oc2pd1CK3odiQ207kHhQbcs+JPIBiQx44kS0oNmRLIhGbkc7t+DYUG77t5PwAig35wIl8CMWGfOhEHkGxIY+cyK+g2JBfOZG3oNiQt5zIO1BsyDtOZAeKDdlxIg+h2JCHTuQuFBtyVyKrV2oGJSU6sWNVbkG9zAMtRQItW075bpJ1tGFveqzpfgXWvap34NOO3fHQaVSB3fWYdycVWPfM2wMbace6bdFt2k1s2NtO7D7MADt234n9QjyvwH7hsdJeVGDda+0A+tmxbut7F67s2LtO7D2o2bHuPeo+tNix9z12jEkFtuXEPhAvK7A+Vj+rwLrtfhvsih3r3qc60N+O9bGmswqs254egQdjx7p3q0fQasc+cmIfi7MK7GMn9kuw7nbslx477JsKrNpjL9EOMiR/JIIVW0ctLFYl1iZALXTwT4q9JSHfuAftLsywwAwJM3Ii9grEnifioEAceMuVF3Y0J3/XzaVdINqeiF6xN2Ft6uw/KPpjLfFA7BSInSVEnUeKz1qN5ZS8C9XiQk6LnQtrPmNKC/uNtUjOh3rLqxD3Swie289o5l+jaAkjKNRUHbVnxR7PyICu6xCvKHpTo1Q83LhpYRVM1JkT1bOgek7UawvqtRM1s6BmTtSpBXXqROmVb+K6HjNA6x+fxZyueAawj1xdAvAKtmDXuQ1rNID50wIv8CG13IfPNsXerlInGUbzuE9iluNJyRJnUJuLNWjXUeEOxdcJrbAIJOOe92WMj1eY25jLNcdWeFHs5EGRMfGnE5M8w4IOeosBradmdO5Qy4K8O641w98u1r2qNcPvksYX5MVzrRl+KqWfnkP2jsR2zoFtw2qaSO3relManH9hGqp+iXZdtLj4VEdyziC9s4b09+WT2T/Hc9mmGutH15vRyI3x5aXxNaGh9Zwbem5GBb0n9npVLWg8krGMe3W9qQwp7aJjKYe+avpksM9APhlVb0ajBR7XNsXcc6PedPZOitHoejMaR4Lzngvy5FW9GY0hXbM+dL0ZDcy2hDLO1/Wmlh01wLGzrje16mPKAmMOiOc8t2ivKCM/aSapxeQf1GdrTJ9/dR/DnM3TIkaop6R922o6vWIvq5dI+QsRWLVpQznQv5gZPliZxlxsOuMrlmFa2t9X6eg9HjV/AFoMYPXzGYArZ56AhCongdY7AYobzqirPDKF23TicJacLKG6snXq9BY1X84alduOqdUVl+nRaj12yV7nNPcm5BMekGZdejiofMJVFF0aOihpyE2vie7eyPVa1v66EzdZQkyKmdanEyE+SauPU21abxs6viJPeaZQ+MxHz1/MNp9Ia4MxT0q2CGWp42n2U3kksw331WtC57j5XkBPFO3VKVmNmE6kcmcUqrLF7I3P6VrTPqQzOeTBNPrwHANJZSL41Ayz6JhPD8iimvbWxRv1pTJ0XM/J6ip7XI8eGuihBd08xtmGHeMe1DoQMxzCVccjyrlU6ColjWfiw+J0NKUnWB/RJyULqWiwvYlKFrIuyn5WovIK0DgbOEr3p7FMR+G7K5TcUb9NHh27li3/FTq5VefbIc3x6tlcnYkZENdN4hrQquFTXb5a5sASzK13Nsl/rR8l8mvCEW2oi+tTgzPrZUwn/hFFsBPyjBNaba7VUe5t5qeW7yhOLaHOzvE0OyULGZD9C2B/SmlOBvRrvjugTtDZIiRkI33sTlx4NzZfJ3bOMe3HxYLfatDzLSJbNiP+iq65unKaixwx8D6wWJrbSicH5AtGxDWT1l2v7frdB5H6PQlzljBFPVeuEv8P6K/6VfNkbWVGoIbxCeTS1tmeR0oxC+oopF2+3gapvqaU7xcyPJVS6/1Py/R+SbIdirhQHtytB8C5T9fMC2dJRnLnK314H63L5iLlyZIecbQnFMWz3R/KHRjlvka75BqtuS7NkiHMgmkRRai+rizyMt96XmXqfrTz/wt1reuy1pBiIHQGlzXkyu9HFK2ZUiYwq3n+vqDVZNd6ttSrns+Y5uLIWMtvofXn8FfJra796PRKVuEmzQGmoK+0RrglWOnhx+tmiZeamYqWvtb89JxUvcyW88TXbN10jH3amEqLZs2ZzFqo+nloPDdoPPfUYYfOGrUWVbuyRMfO2KIjTyt9+TXh1mlAeeak7PbIFCr2kNKMpfyoDpxU3TG+Qr1x0lp30gphtZqnAeaa90Ha1/ry6n5b7O6BuEW+TZ88MI5fBrRKY/K5VGt9pMYUkPMNaV/N1d+lFuTeIwuKlPk9TlwxfOrUp7IoJP2l3NlSsvPaIqj3ll7JPsrGdqn+0QpyRGsip3WpEDeoRyTlN+UIlizSdcPnCCjzH5JPxX5Hfcxs9tbPJCj5Ezre5FWleXGkMCb9uzJv+yvR674RvwYUE86kd90DWs2fMFJgjMok2D3LnJ4Q7nJ8ksAebY/s56qd4lO8sSHRdZJ6Lj7zsDEc9eq5bs4tNWI1tl9BT9S6fuq2Hm5+iTdHF7/znOiFtKuNpI86X7o+H61Q7nLl6zo9zJb4an3MqI8ZWegor4zpik+9ubBEzbgwxodLs1E0kb+Z5E1k5tMpX8qqt6JczjSwjXlG8ZLrPVBE2Ly7q1Zv7gPHOHor9HqENalxi4sSZuNSmR8wLS1mpS6u7EPcerF2N0qMnahqp1DUzd1C22+2kBFZv0S4cjbc25S9W4pS3FkYptAX/EZvVXxo0vwUCv4NhC06VBx9codt8G+3xLbY/Qbehngp65zRDKgFbcFgKfYO5TjLPep19NKgbtL34eDPIwZdu6SPaSdtKjtTdktuUven/4qsQCYip/S6Z/MxmFzcI1nl1GQ8MVk292hiob6L03QsioPPSMpc/PnwuYZrFCdCfaep2RgUdfcIyhya8FDvMfg9c927OS+TU72+Vrn48uBdQJ24KBye/FXHKrqfj4XKjCfyzXNA63BSQ13tFv/rOBQfzak5L19uOX3X7LnHU+d+kczIoj/cfM1obj6zuZqjP8+0GJ32luz82O8LGj2p1BjNN08f/VE9BxSvueA8qFs6xpuzSMvrSwXPBWwypOI/4q8X3N9GeFnQqJKjCSV1TlFNTfVwU1PfuLSNTt3zkUnTqZKpTE3HEW16I3Zb7Itb8LtdeIBN3w7l71LyJ2Lt358dQOsJWQ+VRefMQZfaIsp+6FO0AV3r92erJMZ3efnd3g604Fn4AbXie773qD++69spja36GyS81u+KVAxKEcny6Z5eVz0YQfnkjXNA6nu+Ab1Lz1ksfvNs5HG2qN6fWpZoTnfcbxb0KvE9Q8o+zdWJPKvHkwN8wz4s8kOB+A21hdLO457r4tyq5Nxa4pyTdsoczox79e9mVXHZNrgMitzZqeyXUpytz/Pqc6M7lVz4HfR6/LAGPzSkbJP2X1AknIn6bN6shuZMymSesI6FykSyHjDODIvnXR/ZntbwOvUY/51K9B1D0j2QpUf574BO2DKil0jd7JL0/KZjfSb1do208nuU9N8NPqGfgCsf35CVTzaK/25wtHl947fXP3pwY+3zm/L/HLwrfiZ+Ia7CGv9YfA7UWuIQOPxB/E38Xfxj6/dbf9z609afues7FyTmp6L0s/WX/wJnI7hT</latexit> min x2Rd 1 2 kAx yk2 + kxk1 <latexit sha1_base64="lLsRnvUWJkY/RQ0TaBM4L4cAAjc=">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</latexit> Jointly convex <latexit 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over <latexit 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parameterization <latexit 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min x2Rd,⌘2Rd + 1 2 ||Ax y||2 + 1 2 X i x2 i ⌘i + ⌘i <latexit 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Minimization on ⌘: <latexit sha1_base64="+2GPREQpEwIVrYJm4P1duouGq8A=">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</latexit> Minimization on x: <latexit sha1_base64="XoMHG/upk4SQvsnTOC9fMQMDdXI=">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</latexit> ⌘ |x| <latexit 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x (A>A + diag(⌘ 1)) 1A>y <latexit 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⌘? = |x|
  12. 1 2 2 Quadratic variational formulation: k k1 = inf⌘>0

    1 2 P i ⌘ 1 i | i | 2 + 1 2 P i ⌘ i . 7 / 49 <latexit 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“⌘-trick” Iterative Reweighted Least Squares <latexit sha1_base64="snzG/SUNhxJOSDZedYIkBqAlzNM=">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</latexit> |x| = inf ⌘>0 1 2 x2 ⌘ + 1 2 ⌘ <latexit sha1_base64="SaxMCG/AIDgBrgxMVRkSten/UyU=">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</latexit> min x2Rd 1 2 kAx yk2 + kxk1 <latexit sha1_base64="lLsRnvUWJkY/RQ0TaBM4L4cAAjc=">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</latexit> Jointly convex <latexit 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over <latexit 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parameterization <latexit 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min x2Rd,⌘2Rd + 1 2 ||Ax y||2 + 1 2 X i x2 i ⌘i + ⌘i <latexit 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Minimization on ⌘: <latexit sha1_base64="+2GPREQpEwIVrYJm4P1duouGq8A=">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</latexit> Minimization on x: <latexit sha1_base64="XoMHG/upk4SQvsnTOC9fMQMDdXI=">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</latexit> ⌘ |x| <latexit 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x (A>A + diag(⌘ 1)) 1A>y <latexit sha1_base64="i/Ola8a7r4H3a3v882xa+1W4QCI=">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</latexit> Problem: does not converge (F non-smooth). <latexit 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Regularisation: <latexit 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Minimization on ⌘: <latexit 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⌘? = |x|
  13. Variational Representation <latexit sha1_base64="LvhqKSr3hik5zgcAuhWUDO43Vis=">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</latexit> convex <latexit 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non-smooth <latexit 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    smooth <latexit sha1_base64="wUonO5puT+guKFuVkv+9v7DNgFg=">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</latexit> non-convex <latexit sha1_base64="7xh8rA8zANqdhqPchx9bfdGk53k=">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</latexit> |x| = min uv=x u2 + v2 2 <latexit sha1_base64="sYSTv3M6+H+nMT9S9CDXT7t+qxY=">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</latexit> u? = sign(x)v? = p |x| <latexit sha1_base64="snzG/SUNhxJOSDZedYIkBqAlzNM=">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</latexit> |x| = inf ⌘>0 1 2 x2 ⌘ + 1 2 ⌘ <latexit 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⌘? = |x| <latexit 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u , p ⌘ <latexit 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v , x/ p ⌘
  14. Variational Representation <latexit sha1_base64="LvhqKSr3hik5zgcAuhWUDO43Vis=">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</latexit> convex <latexit 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non-smooth <latexit 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    smooth <latexit sha1_base64="wUonO5puT+guKFuVkv+9v7DNgFg=">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</latexit> non-convex <latexit sha1_base64="7xh8rA8zANqdhqPchx9bfdGk53k=">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</latexit> |x| = min uv=x u2 + v2 2 <latexit sha1_base64="sYSTv3M6+H+nMT9S9CDXT7t+qxY=">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</latexit> u? = sign(x)v? = p |x| <latexit sha1_base64="snzG/SUNhxJOSDZedYIkBqAlzNM=">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</latexit> |x| = inf ⌘>0 1 2 x2 ⌘ + 1 2 ⌘ <latexit 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⌘? = |x| <latexit 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Alternate form: <latexit sha1_base64="npZo7/vkol/v8V2t/Lnba4nbquk=">AABB93ictVzdchS5FRabv4X8scllbjoxpNgU6xgvyWZrK1VrbGO8GDDM2LC7A1TPTHvc0DM9dPfYwKyfJBe5S+U2T5DKbfIEeYPkKq+Q8yO11DPqltohqGyrNfrOOTotHZ1zpKE/TeK8WFv754X3vvXt73z3e+9fvPT9H/zwRz++/MFPDvN0lg2ig0GapNmTfphHSTyJDoq4SKIn0ywKx/0ketx/uYmfPz6JsjxOJ93izTR6Og5Hk/goHoQFND2//JsrvSweHRdhlqWnV4JJWgThOJqEgA+KNAiTIsomYREF43gSj+O3BFt9fnllbXWN/gXLlRuysiLkv/30g+BA9MRQpGIgZmIsIjERBdQTEYocytfihlgTU2h7KubQlkEtps8jcSYuAXYGvSLoEULrS/g9gqevZesEnpFmTugBcEngJwNkIK4CJoV+GdSRW0Cfz4gyttbRnhNNlO0N/O1LWmNoLcQxtLpwqqcvDsdSiCPxOxpDDGOaUguObiCpzEgrKHlgjKoAClNow/oQPs+gPiCk0nNAmJzGjroN6fN/UU9sxeeB7DsT/yYpr0IJREeOPi0phOKE6Af0NmfwGcuTAOcRUIjkGLF2Sroe0+gn0H8O7fehnFFN6aQPZU6tZ43ITSg25KYTuQPFhtxxIveg2JB7TuQ+FBtyXyIRm5HO7fgOFBu+4+T8EIoN+dCJfATFhnzkRB5CsSEPncivoNiQXzmRt6HYkLedyLtQbMi7TmQXig3ZdSIPoNiQB07kNhQbclsi61dqBiUlOrFjVW5AvcoDLUUCLRtO+W6RdbRhb3ms6UEN1r2qt+CvHbvlodOoBrvtMe+OarDumbcDNtKOdduiO7Sb2LB3nNhdmAF27K4T+4V4UYP9wmOlvazButfaHvSzY93W9x482bH3nNj7ULNj3XvUA2ixYx947BjTGuy+E/tQvKrB+lj9rAbrtvsdsCt2rHuf6kJ/O9bHms5qsG57eggejB3r3q0eQ6sd+9iJfSJe12CfOLFfgnW3Y7/02GHf1mDVHnuJdpAR+SMRrNgmamG5KrE2BWqhg39S7i0J+cZ9aHdhRiVmRJixE7FTInY8EXslYs9brry0ozn5u24unRLR8UT0y70Ja4Wz/7Dsj7XEA7FVIrYWEE0eKb5rNZYT8i5UiwtZlDsX1nzGlJb2G2uRnA/NllchHlQQPLePaeZfp2gJIyjUVBO143KPZ2RAz02IU4re1CgVDzeuKK2CiXrtRPUtqL4T9caCeuNEzSyomRN1YkGdOFF65Zu4nscM0PrHdzGnJ54B7CPXlwC8gg3Yde7AGg1g/uyDF/iIWh7A3w7F3q7SJBlG87hPYpbjacUSZ1CbixVo11HhFsXXCa2wCCTjng9kjI9PmNuYyzXHVvis3MmDMmPiTycmeUYlHfQWA1pP7ejcpZYz8u641g5/p1z3qtYOv00aPyMvnmvt8IWUvjiH7F2J7Z4D24HVNJXa1/W2NDj/wjRU/RLtumhx8a2O5ZxBeq9b0t+Vb2b3HO9lk2qsH11vRyM3xpdXxteGhtZzbui5HRX0ntjrVbWg9UgmMu7V9bYypLSLTqQc+qntm8E+Q/lmVL0djX3wuDYp5p4b9bazd1qORtfb0TgUnPc8I09e1dvRGNEz60PX29HAbEso43xdb2vZUQMcO+t6W6s+oSww5oB4znOL9ooy8pNmklpM/kFztsb0+Zf3MczZPCtjhGZK2retp9Mv97JmiZS/EIFVK1rKgf7FzPDBqjTmYt0ZX7EMRWV/X6aj93jU/B5oMYDVz2cArpx5AhKqnARa7wQo3nBGXdWRKdy6E4ez5GgB1ZOthdNb1Hw5a1Rte06trrhMj1brsUf2Oqe5NyWfcI8069LDXu0brqPo0tBeRUNuem1091au16r215y46QJiWs60AZ0I8Ulac5xq03rH0PFVecpTQOEzHz1/Mdt8JK0Nxjwp2SKUpYmn2U/lkcw23FevC53j5s8CeqNor07IasR0IpU7o1CVLWZvfE7PmvYBnckhD6YxgPcYSCpTwadmmEXHfHpAFtW0ty7eqC+VoeN6TlZX2eNm9MhAjyzo9jHOJuwY96HWhZjhAJ66HlHOpVJXKWk8Ex+Vp6MpvcHmiD6pWEhFg+1NVLGQTVH2cYXKKaBxNnCU7k9jkY7C95YouaN+mzw6dq1a/qt0cqvOt0Oa4/WzuT4TMySu68Q1oFXDp7r8tMiBJZhbP1kn/7V5lMivDUe0oS6uzwzOrJcJnfhHFMFOyTNOaLW5Vke1t5mfWvxEcdoX6uwcT7NTspAB2b8A9qeU5mRAP+bdAXWCzhYhIRvpY3fi0rux+Tqxc45pPy4WfKtBz7eIbNmM+Cu65urKaS5yxMD7wNnC3FY62SNfMCKumbTuem037z6I1PckzFnCFPVcuUb8P6Tf6kfNk5WlGYEaxjeQS1tnex8pxSyoo5B2+WYbpPqaUl4pZXgmpdb7n5bpSkWyLYq4UB7crYfAeUDPzAtnSUZy50t9eB9tyuYi5emCHnG0RxTFs90fyR0Y5b5Ou+QKrbkezZIRzIKijCJUX1cWeZFvM68qdT/a+f+FutZ1VWtIMRA6g8sacuX3I4rWTCkTmNU8f1/SarJrPVvo1cxnQnNxbKzlb6D15/Bbya2e/ej0K1bhFs0BpqCftEa4JVjq4cfrVoWXmpmKln7W/PScVL3MlvPE12zddIx90prKPs2a1zJroernofHCoPHCU4ddOmvUWlTtyhI9d8YWXXla6cuvDbduC8ozJ2W3R6ZQsYeUZizlR3XopOqO8RXqrZPWmpNWCKvVPA0w17wP0r7WF1f3N+XuHojb5NsMyAPj+GVIqzQmn0u1NkdqTAE535T21Vz9PWpB7n2yoEiZ73HiiuFTpwGVs1LSX8qdLSU7ry2Curd0KvsoG9uj+sdLyDGtiZzWpULcpB6RlN+UI1iwSKuGzxFQ5j8kn4r9juaY2eyt30lQ8Sd0vMmrSvPiSGFC+ndl3naXotddI34NKCacSe+6D7Tav2GkwBiVSbB7ljm9Idzl+CSBPdo+2c9lO8WneBNDolWSei5+72FjOOrVc92cW2rEamy/gp6odf3WbT3c/BJvji5+5znRC2lXG0sfdb7wfD5aodzlqs9Nepgt8NX6mFEfM7LQUV4V0xOfeXNhidpxYYwPl3ajaCN/O8nbyMynU76UVW9FuZppYBtzTPGS6x4oImze3TWrN/ehYxz9JXp9wprUuMVFCbNxqcwPmJYWs1IXl/Yhbr3YuBslxk5Ut1Mo6uZuoe03W8iIrF8iXDkb7m3K3qtEKe4sDFMYCL7RWxcfmjQ/g4K/A2GLDhVHn9xhB/zbDbEptt/BbYhXss4ZzYBa0BYMF2LvUI6z2qNZR68M6iZ9Hw7+PGLQtUv6mHbStrIzZbfkJnV/+qdkBTIROaXXPduPweTiHskypzbjicmyuUcTC/VdnLZjURx8RlLl4s+HzzVcozgS6jtN7cagqLtHUOXQhoe6x+D3znXv9rxMTs36Wubiy4N3AXXionB48lcfq+h+PhYqM97Iu+eA1uGogbraLf7XcSg+mlN7Xr7ccvqu2QuPt879IpmRRX+4/ZrR3Hxmcz1Hf55pOTrtLdn5sd8XtHpTqTGad08f/VE9BxSvueA8qFs6xpuzSMvrSwXPBWwypOI/4q8X3N9GeFXSqJOjDSV1TlFPTfVwU1PfuLSNTn3mI5OmUydTlZqOIzp0I3ZT7Irb8LNZeoBtb4fydyn5L2Lt358dQusRWQ+VRefMQY/aIsp+6FO0IT3r+7N1EuNdXr7b24UWPAvfo1a853uf+uNd325lbPXfIOG1fk+kYliJSBZP9/S66sMIqidvnANS3/MN6C49Z7H45tnY42xR3Z9alGhOn7hvFvRr8X1DygHN1ak8q8eTA7xhH5b5oUD8mtpCaedxz3Vx3q/lvL/AOSftVDm8Nj5rvptVx2XT4DIsc2cnsl9KcbY+z2vOjW7VcuE76M34UQN+ZEjZIe2/pEg4E83ZvFkDzZmUyTxhnQiViWQ9YJwZlu+7ObI9aeB14jH+u7Xou4akOyBLn/LfAZ2wZUQvkbrZJun5pmNzJvVOg7Tye5T0vxt8Sv8CrnxyU1Y+vVH+7waH66s3frv68cP1lc9vyf/n4H3xM/ELcQ3W+Cfic6C2Lw6Awx/E38TfxT823mz8ceNPG3/mru9dkJifisq/jb/8F7HWtu8=</latexit> ! not amenable to alternate minimization. <latexit sha1_base64="ykevw/cChS0JUUVK7j+Mz5LLXmM=">AABC83ictVxbdxTHEW6cmyE3nDzmZRKZHIixImQc28eHc4wuCBkBgl0JbBY4exktC7M7y94QLPoN+QF5y8lrHvMa/w7/g+QpfyF16Z7u2e2Z6lGI5kjb09NfVXVNd3VVda9aw6Q3nqytfX/mvR/88Ec//sn7Z8/99Gc//8Uvz3/wq8NxOh2144N2mqSjh63mOE56g/hg0psk8cPhKG72W0n8oPViE58/mMWjcS8d1Cevh/HjfrM76B312s0JVD09f+nt8dvoWtTo9wZP543pk/Uo+jhqzODzWnR8ElHNR1Tx9PzK2uoa/UTLhSu6sKL0z376QfS9aqiOSlVbTVVfxWqgJlBOVFON4Xqkrqg1NYS6x2oOdSMo9eh5rE7UOcBOoVUMLZpQ+wL+duHuka4dwD3SHBO6DVwS+B0BMlIXAJNCuxGUkVtEz6dEGWuLaM+JJsr2Gj5bmlYfaifqGdRKONMyFId9magj9Tn1oQd9GlIN9q6tqUxJKyh55PRqAhSGUIflDjwfQblNSKPniDBj6jvqtknP/0UtsRbv27rtVP2bpLwAV6RquvdpRqGpZkQ/orc5hWcsTwKcu0Ah1n3E0ivSdZ96P4D2c6i/A9cJlYxOWnDNqfakFLkJlw+5KSJ34PIhd0TkHlw+5J6I3IfLh9zXSMSOSOd+fA0uH74mcr4Hlw95T0Teh8uHvC8iD+HyIQ9F5Ldw+ZDfisgbcPmQN0TkLbh8yFsisg6XD1kXkQdw+ZAHInIbLh9yWyOLZ+oIrpTo9IRZeR3KeR5oKRKouS7Kt0HW0YfdCJjT7QKsPKu34NOP3QrQaVyA3Q4Yd0cFWHnk7YCN9GNlW3STVhMf9qaI3YUR4Mfuitiv1fMC7NcBM+1FAVaea3vQzo+Vre9tuPNjb4vYO1DyY+U16i7U+LF3A1aMYQF2X8TeUy8LsCFWf1SAle1+DeyKHyuvU3Vo78eGWNNpAVa2p4fgwfix8mr1AGr92Aci9qE6LsA+FLHfgHX3Y78JWGHfFGDNGnuOVpAu+SMxzNgyas1sVmJpCNSaAv8kW1sS8o1bUC9huhmmS5i+iNjJEDuBiL0MsRcs1zizo2Pyd2UutQxRC0S0srUJSxOxfSdrj6UkALGVIbYWEGUeKb5r05cZeRemRkJOspULSyF9SjP7jaVYj4dyy2sQd3MIHtvPaORfpmgJIyjUVBm1Z9kaz8iI7ssQryh6M700PGTcJLMKLupYRLU8qJaIeu1BvRZRUw9qKqJmHtRMRNmZ7+IaASPA6h/fxZzueASwj1x8ReAVXIdV5ybM0QjGzz54gfep5i581ij2lq4yyTCax3USsxyPc5Z4BKW5WoF6GxVuUXyd0AyLQTJueVfH+HiHuY25nnNshU+ylTzKMibhdHokTzejg95iRPOpGp1bVHNC3h2XquFvZvPelKrht0njJ+TFc6kafqKln5xC9rrG1k+BrcFsGmrt23JVGpx/YRqmfI5WXbS4+Fb7eswgveOK9Hf1m9k9xXvZpBLrx5ar0Rg7/Rvn+leFhtXz2NFzNSroPbHXa0pR5Z4MdNxry1VlSGkVHWg57F3VN4NtOvrNmHI1GvvgcW1SzD13ylVH7zDrjS1Xo3GoOO95Qp68KVej0aV71octV6OB2ZamjvNtuaplRw1w7GzLVa36gLLAmAPiMc811isakZ801dR65B+UZ2tcn395HcOczZMsRiinZH3bYjqtbC0rl8j4CzFYtUlFOdC/mDo+WJ7GXK2L8RXLMMmt78t07BqPmt8DLUYw+3kPQMqZJyChyUmg9U6A4hUx6sr3zODWRRyOkqMFVEPXTkRv0fLlrFG+7inVSnGZ7a3VY4Ps9ZjG3pB8wj3SrKSHvcI3XERR0tBeTkMyvSq6e6Pna177ayJuuIAYZiOtTTtCvJNWHqf6tF5zdHxB7/JM4OI9Hzt+Mdt8pK0Nxjwp2SKUpYyn287kkdw6XFcvK5vj5mcRvVG0VzOyGj3akRqLUajJFrM3Pqd7S/uA9uSQB9Now3uMNJWh4l0zzKJjPj0ii+raW4k36stk6Lg8Jqtr7HE5uuugux509RhnE1aMO1CqQ8xwAHf1gCjnXKarlDQ+Uh9nu6MpvcHyiD7JWUhDg+1NnLOQZVH2sxyVV4DG0cBRejiNRToG31iiJEf9Pnls7Jq3/Bdo59bsbzdpjBeP5uJMTIe4rhPXiGYN7+ry3SIHlmDufbJO/mt5L5FfFY5oQyWuTxzOrJcB7fjHFMEOyTNOaLZJsyPf2s1PLT4xnPaV2TvH3eyULGRE9i+C9SmlMRnRr3t2wOygs0VIyEaG2J1e5t34fJ2eOMasH9dTfKrBjreYbNmU+Bu67uwa01jkiIHXgZOFsW10ske+YExcR9q627ldvvog0p6TcEcJU7Rj5SLxv0R/za8ZJytLIwI1jG9grG2d732kFLOgjpq0ypfbINPWlfLDTIYnWmq7/lmZPsxJtkURF8qDq3UHOLfpnnnhKBmR3OOlNryOlmVzkfJwQY/Y2yOK4tnud/UKjHJfplVyheZcg0ZJF0bBJIsiTFspi7zIt5xXnnoY7fH/hbrVdV5rSDFSNoPLGpLy+zFFa66UCYxqHr8vaDb5tT5aaFXOZ0Bjse/M5bdQ+1v4a+Q292F0WjmrsEFjgCnYO6sRromWWoTx2sjxMiPT0LL3lp8dk6aVW3Oa+Jqtm42xZ5Wp7NOoOdZZC1M+DY3nDo3ngTqs016j1aKpN5boqRhb1PVuZSi/KtzqFShPRcqyR2ZQvQAp3VgqjGpHpCrH+Ab1RqS1JtJqwmx1dwPcOR+C9M/1xdn9NlvdI3WDfJs2eWAcv3RolvbI5zK15ZEaU0DOV7V9dWd/g2qQe4ssKFLmc5w4Y3jXqU3XSSbp7/XKlpKdtxbBnFt6pdsYG9ug8idLyD7NiTHNS4O4Si1iLb8rR7RgkVYdnyOizH+TfCr2O8pjZre1fSdRzp+w8SbPKsuLI4UB6V/KvO0uRa+7TvwaUUw41d51C2hVf8NIgTEmk+D3LMf0hnCV450E9mhbZD+X7RTv4g0ciVZJ6rm6FmBjOOq1Y90dW6bHpm9/gJaodfvWfS1kfkkwR4nfaXb0mrSq9bWPOl+4Px2tpl7l8vdlepgu8LX6mFIbN7KwUV4e01BfBnNhiapxYUwIl2q9qCJ/NcmryMy7U6GUTWtDOZ9pYBvzjOIl6RwoInze3UWvN3dJ6EdriV6LsC41rpEoYTYu1fkB19JiVurs0jrEtWdLV6PEWYmKVgpD3V0trP1mCxmT9UuUlLPh1q7sjVyUImdhmEJb8YneovjQpfklXPg3Ur7o0HAMyR3WwL+9rjbV9js4DfFSlzmjGVEN2oLOQuzd1P3MtyjX0UuHuks/hEM4jx7oWpK+RytpVdmZsiy5Sz2c/iuyAiMVi9LbltX74HKRe7LMqUp/emTZ5N70lPkuTtW+GA4hPclzCefD+xpSL46U+U5TtT4Y6nIP8hyq8DDnGMLeuW1dnZfLqVxfy1xCefAqYHZcDA53/opjFdsuxEKNnDfy7jmgdTgqoW5Wi/+1H4aP5VSdVyi3MX3X7HnAW+d2sc7Ioj9cfc5YbiGjuZhjOM806531lvz82O+LKr2p1OnNu6eP/qgdA4bXXHEeVJaO8e4osvKGUsF9AZ8MqfqP+u6M/G2ElxmNIjmqUDL7FMXUTAuZmvnGpa935lmITJZOkUx5ajaOqNGJ2E21q27A72bmAVY9HcrfpeRPxPq/P9uB2iOyHiaLzpmDBtXFlP2wu2gdurfnZ4skxrO8fLa3DjW4F75HtXjO9w61x7O+9Vzfir9BwnP9tkpVJxeRLO7u2XnVgh7kd944B2S+5xvRWXrOYvHJs37A3qI5P7Uo0ZyeyCcLWoX4liNlm8bqUO/V484BnrBvZvmhSP2R6prazuOaK3HeL+S8v8B5TNrJczh2npWfzSrisulw6WS5s5lul1KcbffzynOjW4Vc+Ax6Ob5bgu86UtZI+y8oEh6p8mzetITmVMvk7rAOlMlEsh4wzmxm77s8sp2V8JoF9P9WIfqWI+kOyNKi/HdEO2wjopdo3WyT9HzSsTyTerNEWvM9Smns8vchOC9h/tfAI8pLtcgKrKnL9LuqPoeW06CZOBNoIq3LmvKJ1mt5xsSeryyj+mkm66cKM0gGBdTpvzx8QT8RFz67qgtfXMn+y8Ph+uqVP61+cu/qylcb+v89vK9+o36nLoKt+0x9BVrdVwfA/8/qH+qf6ruN6cZfNv668Tdu+t4Zjfm1yv1s/P2/q93hmw==</latexit> |x| = min u2 v2=x u2 + v2 <latexit 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u , p ⌘ <latexit 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v , x/ p ⌘
  15. Variational Representation <latexit sha1_base64="LvhqKSr3hik5zgcAuhWUDO43Vis=">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</latexit> convex <latexit 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non-smooth <latexit 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    smooth <latexit sha1_base64="wUonO5puT+guKFuVkv+9v7DNgFg=">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</latexit> non-convex <latexit sha1_base64="7xh8rA8zANqdhqPchx9bfdGk53k=">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</latexit> |x| = min uv=x u2 + v2 2 <latexit sha1_base64="sYSTv3M6+H+nMT9S9CDXT7t+qxY=">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</latexit> u? = sign(x)v? = p |x| <latexit sha1_base64="snzG/SUNhxJOSDZedYIkBqAlzNM=">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</latexit> |x| = inf ⌘>0 1 2 x2 ⌘ + 1 2 ⌘ <latexit 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⌘? = |x| <latexit 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Alternate form: <latexit sha1_base64="npZo7/vkol/v8V2t/Lnba4nbquk=">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</latexit> ! not amenable to alternate minimization. <latexit sha1_base64="ykevw/cChS0JUUVK7j+Mz5LLXmM=">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</latexit> |x| = min u2 v2=x u2 + v2 <latexit sha1_base64="SaxMCG/AIDgBrgxMVRkSten/UyU=">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</latexit> min x2Rd 1 2 kAx yk2 + kxk1 <latexit 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min u,v 1 kA(u v) yk2 + kuk2 2 + kvk2 2 <latexit sha1_base64="VwU4bjbjAw/6TPQPDVxdaVZJlKI=">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</latexit> x = u v <latexit 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, (uivi)d i=1 <latexit 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u , p ⌘ <latexit 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v , x/ p ⌘
  16. Variational Representation <latexit sha1_base64="LvhqKSr3hik5zgcAuhWUDO43Vis=">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</latexit> convex <latexit 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non-smooth <latexit 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    smooth <latexit sha1_base64="wUonO5puT+guKFuVkv+9v7DNgFg=">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</latexit> non-convex <latexit sha1_base64="7xh8rA8zANqdhqPchx9bfdGk53k=">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</latexit> |x| = min uv=x u2 + v2 2 <latexit sha1_base64="sYSTv3M6+H+nMT9S9CDXT7t+qxY=">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</latexit> u? = sign(x)v? = p |x| <latexit sha1_base64="snzG/SUNhxJOSDZedYIkBqAlzNM=">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</latexit> |x| = inf ⌘>0 1 2 x2 ⌘ + 1 2 ⌘ <latexit 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⌘? = |x| <latexit 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Alternate form: <latexit sha1_base64="npZo7/vkol/v8V2t/Lnba4nbquk=">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</latexit> ! not amenable to alternate minimization. <latexit sha1_base64="ykevw/cChS0JUUVK7j+Mz5LLXmM=">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</latexit> |x| = min u2 v2=x u2 + v2 <latexit sha1_base64="SaxMCG/AIDgBrgxMVRkSten/UyU=">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</latexit> min x2Rd 1 2 kAx yk2 + kxk1 <latexit 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min u,v 1 kA(u v) yk2 + kuk2 2 + kvk2 2 <latexit sha1_base64="VwU4bjbjAw/6TPQPDVxdaVZJlKI=">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</latexit> x = u v <latexit sha1_base64="dYUkH7hnSlfCBXN1uYbi20DFxq0=">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</latexit> , (uivi)d i=1 <latexit sha1_base64="my0E+vgeJWmKlzNLs9Rdhsorp4U=">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</latexit> (Sherman–Morrison formula) <latexit sha1_base64="83eKHl+qCDf6euBpfa9tc5tvDvM=">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</latexit> Alternating mimization: <latexit sha1_base64="+8lThvl9GuWuxQI5dWUydgORXrw=">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</latexit> Empirical finding: works better than IRLS (despite non-convex). <latexit 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u (diag(v)A>Adiag(v) + Idd) 1(v A>y) <latexit 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= v A>(Adiag(v2)A> + Idn) 1y <latexit 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v (diag(u)A>Adiag(u) + Idd) 1(u A>y)u <latexit 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u , p ⌘ <latexit 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v , x/ p ⌘
  17. Lasso illustration Evolution of 10 coe cients via ISTA and

    gradien ISTA Noncvx- ISTA : k+1 = SoftThresh k ⌧X > Noncvx-Pro: k+1 = k ⌧rf ( k ). Lasso illustration Evolution of 10 coe cients via ISTA and gradient descent of f . ISTA Noncvx-Pro ISTA : k+1 = SoftThresh k ⌧X >(X k y), ⌧ Noncvx-Pro: k+1 = k ⌧rf ( k ). 12 / 49 . Quadratic For Lasso Numerical
  18. VarPro General Idea <latexit 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Envelope theorem: <latexit sha1_base64="SYQDeQ1yH+gNfM+oH9y/AsAnH/8=">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</latexit> Variational

    Projection: Gene Golub Victor Pereyra <latexit sha1_base64="T67g3m5D/nIqeo47Q/RS6LTWYlE=">AABDAnictVxLk9u4EYY3r7Xz8ibHXJjMOmWnJpOx15v11tZWrefh8azHtmxpxt61bBclcWTalCiTkvzQzi2/Iz8gt1Suqcol1+S+/yA55S+kHwABSiABTpxhaQYE8XU3mkCjuwFNb5LE+XRz89sz733nu9/7/g/eP3vuhz/68U9+ev6Dnx3l6SzrR4f9NEmzh70wj5J4HB1O42kSPZxkUTjqJdGD3ottfP5gHmV5nI470zeT6PEoHI7j47gfTqHq6flrxxe780tBd5rF4XiYRC+DGxe7syfdfBpm+GQdn34edGejeLzozk7oMVY+Pb+2ubFJP8Fq4bIsrAn500o/CL4VXTEQqeiLmRiJSIzFFMqJCEUO1yNxWWyKCdQ9Fguoy6AU0/NInIhzgJ1BqwhahFD7An4P4e6RrB3DPdLMCd0HLgl8MkAG4gJgUmiXQRm5BfR8RpSxtor2gmiibG/gb0/SGkHtVDyDWhdOtfTFYV+m4lhcoz7E0KcJ1WDv+pLKjLSCkgdGr6ZAYQJ1WB7A8wzKfUIqPQeEyanvqNuQnv+LWmIt3vdl25n4N0l5Aa5AtGXv04JCKOZEP6C3OYNnLE8CnIdAIZJ9xNIr0vWIej+G9guovwPXCZWUTnpwLaj2pBa5DZcNue1E7sFlQ+45kQdw2ZAHTmQLLhuyJZGIzUjndnwbLhu+7eR8Dy4b8p4TeR8uG/K+E3kElw155ER+DZcN+bUTeQMuG/KGE3kLLhvylhPZgcuG7DiRh3DZkIdO5C5cNuSuRFbP1AyulOjEjll5HcplHmgpEqi57pRvi6yjDbvlMaf7FVj3rN6Bv3bsjodOowrsrse4O67AukfeHthIO9Zti27SamLD3nRi92EE2LH7TuyX4nkF9kuPmfaiAuueawfQzo51W9/bcGfH3nZi70DJjnWvUXehxo6967FiTCqwLSf2nnhZgfWx+lkF1m3322BX7Fj3OtWB9nasjzWdVWDd9vQIPBg71r1aPYBaO/aBE/tQvK7APnRivwLrbsd+5bHCvq3AqjX2HK0gQ/JHIpixddTCYlZiaQLUQgf/pFhbEvKNe1DvwgwLzJAwIydir0DseSIOCsSBt1x5YUdz8nfdXNoFou2J6BVrE5amzvaDoj2WEg/EToHYWULUeaT4rlVf5uRdqBoXclqsXFjy6VNa2G8sRXI81FtehbhbQvDYfkYjf52iJYygUFN11J4VazwjA7qvQ7yi6E31UvFw46aFVTBRr52ongXVc6LeWFBvnKiZBTVzouYW1NyJ0jPfxHU9RoDWP76LBd3xCGAfufoKwCu4DqvOTZijAYyfFniB96nmLvxtU+ztuuokw2ge10nMcjwuWeIMSguxBvU6Ktyh+DqhGRaBZNzyrozx8Q5zGws559gKnxQreVBkTPzpxCTPsKCD3mJA86kZnVtUc0LeHZea4W8W816VmuF3SeMn5MVzqRl+KqWfnkL2jsR2ToFtw2yaSO3rclManH9hGqp8jlZdtLj4VkdyzCC91w3p78s3s3+K97JNJdaPLjejkRv9y0v9a0JD6zk39NyMCnpP7PWqUtC4J2MZ9+pyUxlSWkXHUg591/TNYJuBfDOq3IxGCzyubYq5F0a56eidFL3R5WY0jgTnPU/Ik1flZjSGdM/60OVmNDDbEso4X5ebWnbUAMfOutzUqo8pC4w5IB7zXKO9ooz8pJmkFpN/UJ+tMX3+1XUMczZPihihnpL2bavp9Iq1rF4i5S9EYNWmDeVA/2Jm+GBlGgtxxRlfsQzT0vq+Skev8aj5A9BiALOf9wBcOfMEJFQ5CbTeCVC87Iy6yj1TuCtOHI6S4yVUV9ZOnd6i5stZo3LdU6p1xWW6t1qPXbLXOY29CfmEB6RZlx4OKt9wFUWXhg5KGnLTa6K7t3K+lrW/6cRNlhCTYqT1aUeId9Lq41Sb1tuGji/IXZ4pXLzno8cvZpuPpbXBmCclW4Sy1PE026k8klmH6+q60DlufhbQG0V7NSerEdOOVO6MQlW2mL3xBd1r2oe0J4c8mEYf3mMgqUwE75phFh3z6QFZVNPeunijvlSGjss5WV1lj+vRQwM9tKCbxzjbsGLcgVIHYoZDuOt4RDnnCl2lpPFM/LbYHU3pDdZH9EnJQioabG+ikoWsi7Kflai8AjSOBo7S/Wks01H47gold9Rvk0fHrmXLf4F2btX+dkhjvHo0V2diBsT1CnENaNbwri7fLXNgCRbWJ1fIf63vJfJrwhFtqIvrE4Mz62VMO/4RRbAT8owTmm2u2VFubeanlp8oTi2h9s5xNzslCxmQ/QtgfUppTAb0Mc8OqB10tggJ2UgfuxMX3o3N14mdY0z7cbHgUw16vEVky2bEX9E1Z1dOY5EjBl4HTpbGttLJAfmCEXHNpHXXc7t+9UGkPidhjhKmqMfKReJ/iX6rjxonaysjAjWMbyCXts72PlKKWVBHIa3y9TZItTWl/LCQ4YmUWq9/WqYPS5LtUMSF8uBqPQDOfbpnXjhKMpI7X2nD62hdNhcpT5b0iL09piie7f5QrsAo9zqtkms057o0SoYwCqZFFKHaurLIy3zreZWp+9HO/y/Uta7LWkOKgdAZXNaQK78fUbRmSpnAqObx+4Jmk13r2VKrej5jGosjYy5/A7W/hN9KbnXvR6dXsgpbNAaYgr7TGuGaYKWFH6+tEi81MhUtfa/56TGpWpk1p4mv2brpGHvemEqLRs1rmbVQ5dPQeG7QeO6pww7tNWotqnpliZ46Y4uO3K305deEW6cB5ZmTstsjU6jYQ0ozlvKjOnBSdcf4CvXWSWvTSSuE2WruBphz3gdpn+vLs/ubYnUPxA3ybfrkgXH8MqBZGpPPpWrrIzWmgJyvSvtqzv4u1SD3HllQpMznOHHG8K5Tn66TQtJfy5UtJTuvLYI6t/RKtlE2tkvlj1aQI5oTOc1LhbhKLSIpvylHsGSRNgyfI6DMf0g+Ffsd9TGz2Vq/k6DkT+h4k2eV5sWRwpj078q87a9Er/tG/BpQTDiT3nUPaDV/w0iBMSqTYPcsc3pDuMrxTgJ7tD2yn6t2infxxoZEGyT1QnzuYWM46tVj3Rxbqseqb7+Blqh1/dZtLdz8Em+OLn6n2dELaVUbSR91sXR/OlqhXOXK93V6mC3x1fqYURszstBRXhnTFZ95c2GJmnFhjA+XZr1oIn8zyZvIzLtTvpRVa0W5nGlgG/OM4iXXOVBE2Ly7i1Zv7pKjH70Vej3CmtS4xkUJs3GpzA+YlhazUmdX1iGuPVu7GiXGSlS1Uijq5mqh7TdbyIisXyJcORtubcreLUUp7iwMU+gLPtFbFR+aND+DC38HwhYdKo4+ucM2+LfXxbbYfQenIV7KMmc0A6pBWzBYir1D2c9yi3odvTSom/R9OPjziEHXLuljWkmbys6U3ZKb1P3pvyIrkInIKb1u2bwPJhd3T1Y5NelPTJbN3ZtYqO/iNO2L4uDTkzIXfz68r+HqxbFQ32lq1gdF3d2DMocmPNQ5Br93rls352VyqtfXKhdfHrwKqB0XhcOdv+pYRbfzsVCZ8UbePQe0Dsc11NVq8b/2Q/HRnJrz8uWW03fNnnu8dW4XyYws+sPN54zm5jOaqzn680yL3mlvyc6P/b6g0ZtKjd68e/roj+oxoHgtBOdB3dIx3hxFWl5fKrgvYJMhFf8Rfzvj/jbCy4JGlRxNKKl9impqqoWbmvrGpa136pmPTJpOlUxlajqOaNOJ2G2xL27AZ7vwAJueDuXvUvJfxNq/PzuA2mOyHiqLzpmDLtVFlP3Qu2gDutfnZ6skxrO8fLa3AzW4F35AtXjO9w61x7O+nVLfqr9BwnP9tkjFoBSRLO/u6XnVgx6Ud944B6S+5xvQWXrOYvHJs5HH3qI6P7Us0YKeuE8W9CrxPUPKPo3Vidyrx50DPGEfFvmhQPyO6kJp53HNdXFuVXJuLXHOSTtlDq+NZ/Vns6q4bBtcBkXubC7bpRRn6/28+tzoTiUXPoNejx/W4IeGlG3S/guKhDNRn82b1dCcSZnMHdaxUJlI1gPGmWHxvusj23kNr7lH/29Vom8Zku6BLD3Kfwe0w5YRvUTqZpek55OO9ZnUmzXSqu9RusYufx+C8xLqfw08orxUj6zAplinz4a4Bi1nXjNx7qCJtNYl5ROp1/qMiT5fWUf140LWjwVmkBQKqNN/efiUfgIufHJVFj69XPyXh6MrG5d/v/HRvatrX2zJ//fwvviF+JW4CLbuE/EFaLUlDoH/H8XfxT/EP7f+sPWnrT9v/YWbvndGYn4uSj9bf/0vquPohA==</latexit> f(v) , F(u?(v), v) = min u F(u, v) <latexit sha1_base64="giqx4/bBN97akGvg1+7OscAW2Xs=">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</latexit> rf(v) = rvF(u?(v), v)
  19. VarPro General Idea <latexit 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Envelope theorem: <latexit sha1_base64="SYQDeQ1yH+gNfM+oH9y/AsAnH/8=">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</latexit> Variational

    Projection: Gene Golub Victor Pereyra <latexit 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f(v) , F(u?(v), v) = min u F(u, v) <latexit sha1_base64="giqx4/bBN97akGvg1+7OscAW2Xs=">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</latexit> rf(v) = rvF(u?(v), v) <latexit 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Implicit di↵erentiation: <latexit sha1_base64="i9gJ4a40lkR4zipG4FoVdDE02ro=">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</latexit> @u?(v) = @2 u F(u?, v) 1@2 u,v F(u?, v) <latexit 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@2f(v) = @2 v F(u?, v) @2 u,v F(u?, v)@2 u F(u?, v) 1@2 u,v F(u?, v)
  20. VarPro General Idea <latexit 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Envelope theorem: <latexit sha1_base64="SYQDeQ1yH+gNfM+oH9y/AsAnH/8=">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</latexit> Variational

    Projection: Gene Golub Victor Pereyra <latexit 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f(v) , F(u?(v), v) = min u F(u, v) <latexit sha1_base64="giqx4/bBN97akGvg1+7OscAW2Xs=">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</latexit> rf(v) = rvF(u?(v), v) <latexit 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Implicit di↵erentiation: <latexit sha1_base64="i9gJ4a40lkR4zipG4FoVdDE02ro=">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</latexit> @u?(v) = @2 u F(u?, v) 1@2 u,v F(u?, v) <latexit 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@2f(v) = @2 v F(u?, v) @2 u,v F(u?, v)@2 u F(u?, v) 1@2 u,v F(u?, v) <latexit 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=) <latexit 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@F 1 = ✓ @2 u F @2 u,v F @2 u,v F @2 v F ◆ 1 = ✓ · · · · · · · · · [@2 v f] 1 ◆ <latexit sha1_base64="tSKv0HuS2kfO5eAwU+AMxohUOqY=">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</latexit> @2 v f is better conditionned than @2 u,v F
  21. Lasso VarPro <latexit sha1_base64="SaxMCG/AIDgBrgxMVRkSten/UyU=">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</latexit> min x2Rd 1 2 kAx yk2

    + kxk1 <latexit sha1_base64="VwU4bjbjAw/6TPQPDVxdaVZJlKI=">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</latexit> x = u v <latexit sha1_base64="A1ZAtxlBHppeP9b83aQLRqnZxYA=">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</latexit> min u,v F(u, v) , 1 kA(u v) yk2 + kuk2 2 + kvk2 2 <latexit sha1_base64="RQJ60M8EfK4pJ9HxTAIUZXby20s=">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</latexit> min v f(v) , min u 1 kA(u v) yk2 + kuk2 2 + kvk2 2
  22. Lasso VarPro <latexit sha1_base64="SaxMCG/AIDgBrgxMVRkSten/UyU=">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</latexit> min x2Rd 1 2 kAx yk2

    + kxk1 Lasso illustration Evolution of 10 coe cients via ISTA ISTA : k+1 = SoftT Lasso illustration Evolution of 10 coe cients via ISTA and gradient descent <latexit 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Forward-backward <latexit 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Lasso VarPro <latexit 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Descend <latexit sha1_base64="VwU4bjbjAw/6TPQPDVxdaVZJlKI=">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</latexit> x = u v <latexit sha1_base64="A1ZAtxlBHppeP9b83aQLRqnZxYA=">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</latexit> min u,v F(u, v) , 1 kA(u v) yk2 + kuk2 2 + kvk2 2 <latexit sha1_base64="RQJ60M8EfK4pJ9HxTAIUZXby20s=">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</latexit> min v f(v) , min u 1 kA(u v) yk2 + kuk2 2 + kvk2 2 <latexit 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Proposition: f is smooth and <latexit sha1_base64="0J9DVzW8My87+/opFWIJ+xpB+3g=">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</latexit> Envelope theorem: <latexit sha1_base64="AnwYxDOZfN2O18xp53N3zZMHoBc=">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</latexit> u?(v) , argminu F(u, v) <latexit sha1_base64="3D9R8zXUx54CQI4IoCxqXDCym5s=">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</latexit> = v A>(Adiag(v2)A> + Idn) 1y <latexit sha1_base64="UIo+BlLZbS+w+U5uLc9U+0P0w58=">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</latexit> rf(v) = rvF(u?(v), v) <latexit 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= 1 u? A>(A(u? v) y) + v
  23. Lasso VarPro <latexit sha1_base64="SaxMCG/AIDgBrgxMVRkSten/UyU=">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</latexit> min x2Rd 1 2 kAx yk2

    + kxk1 Lasso illustration Evolution of 10 coe cients via ISTA ISTA : k+1 = SoftT Lasso illustration Evolution of 10 coe cients via ISTA and gradient descent <latexit 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Forward-backward <latexit sha1_base64="jird3InoZqCM9gZERQ4C24/hO08=">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</latexit> Lasso VarPro <latexit 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