Slide 54
Slide 54 text
C = (x1, . . . , xk
) Hk \ x1
= . . . = xk
Prox
⇥C
(x1, . . . , xk
) = (˜
x, . . . , ˜
x) where ˜
x =
1
k
i
xi
each Fi
is simple
min
x
G1
(x) + . . . + Gk
(x)
min
x
G(x1, . . . , xk
) +
C
(x1, . . . , xk
)
G(x1, . . . , xk
) = G1
(x1
) + . . . + Gk
(xk
)
G and
C
are simple:
Prox
G
(x1, . . . , xk
) = (Prox
Gi
(xi
))
i
More than 2 Functionals