RLR - Regularized Linear Regression
Usage
sol = rlr(x_0,f,A,At, param)
sol = rlr(x_0,f,A,At)
[sol, info] = rlr(..,)
Output parameters
|
sol |
Solution |
|
info |
Structure summarizing informations at convergence |
Description
This function solve minimization problem using forward-backward splitting
sol = rlr(x_0,f,A,At, param) solves:
\begin{equation*}
sol = arg \min_x \|x_0-Ax\|_2^2 + f(x) \hspace{1cm} for \hspace{1cm} x\in R^N
\end{equation*}
where x is the variable.
x_0 is the starting point.
f is a structure representing a convex function. Inside the structure, there
have to be the prox of the function that can be called by f.prox and
the function itself that can be called by f.eval.
A is the operator
At is the adjoint operator of A
param a Matlab structure containing solver paremeters. See the
function solvep for more information. Additionally it contains those
aditional fields:
- param.nu : bound on the norm of the operator A (default: 1), i.e.
\begin{equation*}
\|A x\|^2 \leq \nu \|x\|^2
\end{equation*}
- param.method : is the method used to solve the problem. It can be 'FISTA' or
'ISTA'. By default, it's 'FISTA'.
References:
P. Combettes and J. Pesquet.
A douglas--rachford splitting approach to nonsmooth convex
variational signal recovery.
Selected Topics in Signal Processing, IEEE Journal of,
1(4):564--574, 2007.