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Fast first-order methods for convex optimization with line search
Published on Jan 25, 20125016 Views
We propose accelerated first-order methods with non-monotonic choice of the prox parameter, which essentially controls the step size. This is in contrast with most accelerated schemes where the prox
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Chapter list
Fast first-order methods for convex optimization with line search00:00
Problem under consideration00:12
Examples00:59
First-order methods applied01:17
Prox method with nonsmooth term01:21
ISTA02:08
Fast first-order method03:48
(Fast) Iterative Shrinkage04:52
Iterative Shrinkage Threshholding Algorithm (ISTA)04:57
Fast Iterative Shrinkage Threshholding Algorithm (FISTA)05:46
Find μk · μk-1 such that09:07
Find μk such that10:28
FISTA with full backtracking - 0113:39
FISTA with full backtracking - 0214:48
FISTA with full line search15:26
Computational results16:25
Complexity bounds16:51
Alternating directions method17:02
Alternating direction method (ADM)17:33
A slight modification of ADM18:08
Alternating linearization method (ALM)18:12
Fast ALM (FALM)18:34
Complexity results18:57
Convergence rate for FALM with backtracking19:09