POCS - Projection onto convex sets

Usage

sol = pocs(x_0,F, param);
sol = pocs(x_0,F);
[sol,info] = pocs(...);

Input parameters

`x_0`	Starting point of the algorithm
`F`	Array of function to minimize
`param`	Optional parameter

Output parameters

`sol`	Solution
`info`	Structure summarizing informations at convergence

Description

pocs solves:

\begin{equation*} sol = arg \min_x \|x-x_0\| \hspace{1cm} for \hspace{1cm} x\in \cap_i \mathcal{C}_i \end{equation*}

where x are the optimization variables.

F is a cell array of structures representing the indicative functions of all sets. F{ii}.eval contains an anonymous function that evaluate how far is the point x to the set ii. F{ii}.prox project the point x to the set ii. This .prox notation is kept for compatibility reason.

This function is kept for backward compatibility and is not recommended to be used.