Forward-partial inverse-half-forward splitting algorithm for solving monotone inclusions

TL;DR

This paper introduces a novel splitting algorithm for coupled monotone inclusions that efficiently handles multiple operators and applies to constrained convex optimization problems, demonstrating competitive performance in total variation least-squares tasks.

Contribution

The paper proposes a new splitting algorithm that generalizes existing methods, efficiently manages multiple operators, and applies to complex constrained convex optimization problems.

Findings

Algorithm requires two Lipschitzian operator computations per iteration.

The method is effective for solving constrained total variation least-squares problems.

Performance comparisons show competitiveness with existing methods.

Abstract

In this paper we provide a splitting algorithm for solving coupled monotone inclusions in a real Hilbert space involving the sum of a normal cone to a vector subspace, a maximally monotone, a monotone-Lipschitzian, and a cocoercive operator. The proposed method takes advantage of the intrinsic properties of each operator and generalizes the method of partial inverses and the forward-backward-half forward splitting, among other methods. At each iteration, our algorithm needs two computations of the Lipschitzian operator while the cocoercive operator is activated only once. By using product space techniques, we derive a method for solving a composite monotone primal-dual inclusions including linear operators and we apply it to solve constrained composite convex optimization problems. Finally, we apply our algorithm to a constrained total variation least-squares problem and we compare its performance with efficient methods in the literature.