Faster-FISTA

Matlab code to reproduce the results of the paper

Improving FISTA: Faster, Smarter and Greedier

Jingwei Liang, [Tao Luo]() and Carola-Bibiane Schönlieb, 2018

Quadratic problem

Consider solving the problem below $$ \min{x\in \mathbb{R}^n} ~ \frac{1}{2} |Ax - f|^2 , $$ where $A$ is the Laplacian operator $$ A = \begin{bmatrix} 2 & -1 & & & \ -1 & 2 & -1 & & \ %& -1 & 2 & -1 & & & \ & & \dotsm & & \ %& & & -1 & 2 & -1 & \ & & -1 & 2 & -1 \ & & & -1 & 2 \ \end{bmatrix}{n} . $$

We set $n = 201$.

Error $\	x_{k}-x^\star\	$	Objective function $\Phi(x_{k}) - \Phi(x^\star)$

Linear inverse problems

Consider solving the problem below $$ \min_{x\in \mathbb{R}^n} ~ \mu R(x) + \frac{1}{2} |Ax - f|^2 . $$

$\ell_{1}$-norm

Error $\	x_{k}-x^\star\	$	Objective function $\Phi(x_{k}) - \Phi(x^\star)$

$\ell_{1,2}$-norm

Error $\	x_{k}-x^\star\	$	Objective function $\Phi(x_{k}) - \Phi(x^\star)$

$\ell_{\infty}$-norm

Error $\	x_{k}-x^\star\	$	Objective function $\Phi(x_{k}) - \Phi(x^\star)$

Total variation

Error $\	x_{k}-x^\star\	$	Objective function $\Phi(x_{k}) - \Phi(x^\star)$

Sparse logistic regression

Consider the problem $$ \min{x \in \mathbb{R}^n } \mu |x|{1} + \frac{1}{m} \sum{i=1}^m \log({ 1+e^{ -l{i} h_{i}^T x } }) , $$

Error $\	x_{k}-x^\star\	$	Objective function $\Phi(x_{k}) - \Phi(x^\star)$
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Principle component pursuit

PCP considers the following problem $$ \min{x{l}, x{s} \in \mathbb{R}^{m\times n}}~ \frac{1}{2}|f-x{l}-x{s}|^2 + \mu |x{s}|1 + \nu |x{l}|_* . $$

Original frame	Foreground	Background	Performance comparison

Copyright (c) 2018 Jingwei Liang