Projection and Rescaling Algorithm for Finding Maximum Support Solutions to Polyhedral Conic Systems

Abstract

We propose a simple projection and rescaling algorithm that finds maximum support solutions to the pair of feasibility problems: [Formula: see text] where L is a linear subspace in [Formula: see text] and [Formula: see text] is its orthogonal complement. The algorithm complements a basic procedure that involves only projections onto L and [Formula: see text] with a periodic rescaling step. The number of rescaling steps and, thus, overall computational work performed by the algorithm are bounded above in terms of a condition measure of the above pair of problems. Our algorithm is a natural but significant extension of a previous projection and rescaling algorithm that finds a solution to the full support problem: [Formula: see text] when this problem is feasible. As a byproduct of our new developments, we obtain a sharper analysis of the projection and rescaling algorithm in the latter special case.