Projective method of multipliers for linearly constrained convex minimization

TL;DR

This paper introduces a novel projective multiplier method for linearly constrained convex minimization, leveraging monotone operator algorithms applied to the dual problem, with proven convergence rates and practical applications in TV denoising and compressed sensing.

Contribution

It develops a new projective method based on monotone operator algorithms for constrained convex problems, with established convergence guarantees.

Findings

Convergence rates are proven for the proposed method.

Applications demonstrated in TV denoising.

Effective in compressed sensing problems.

Abstract

We present a method for solving linearly constrained convex optimization problems, which is based on the application of known algorithms for finding zeros of the sum of two monotone operators (presented by Eckstein and Svaiter) to the dual problem. We establish convergence rates for the new method, and we present applications to TV denoising and compressed sensing problems.