Slide 18
Slide 18 text
Algorithm: Proximal Gradient Descent
MFP:
min
⇢,m2C(⇢0,⇢1)
Z 1
0
Z
⌦
km(t, x)k2
2
2⇢(t, x)
+ F(x, ⇢(t, x))dxdt
| {z }
Y(⇢,m)
, min
⇢,m
Y(⇢, m) + XC(⇢0,⇢1)
(⇢, m)
where XC(⇢0,⇢1)
(⇢, m) =
(
+1, (⇢, m) 62 C(⇢0, ⇢1),
0, (⇢, m) 2 C(⇢0, ⇢1).
Proximal Gradient Descent method for MFP:
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:
⇣
⇢k+ 1
2 , mk+ 1
2
⌘
= ⇢k, mk ⌘k
⇢,mY ⇢k, mk ,
| {z }
gradient (forward) descent
easy and fast to compute for di↵erentiable F
⇢k+1, mk+1 = ProjC(⇢0,⇢1)
⇣
⇢k+ 1
2 , mk+ 1
2
⌘
,
| {z }
proximal (backward) descent
=
⇣
⇢k+ 1
2 , mk+ 1
2
⌘
rt,m
1
t,mrt,m ·
⇣
⇢k+ 1
2 , mk+ 1
2
⌘
.
| {z }
independent to the form of F
fast to compute with Fast Cosine Transformation
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