Solving Non-Monotone Inclusions Using Monotonicity of Pairs of Operators

TL;DR

This paper introduces generalized proximal point algorithms leveraging operator pairs' monotonicity to solve non-monotone inclusions, with proven convergence properties under mild conditions.

Contribution

It presents novel algorithms based on warped and transformed resolvents for non-monotone inclusions, extending the applicability of proximal methods.

Findings

Algorithms achieve weak, strong, and linear convergence.

Convergence is established under very mild conditions.

The methods effectively handle non-monotone problems.

Abstract

In this paper, under the monotonicity of pairs of operators, we propose some Generalized Proximal Point Algorithms to solve non-monotone inclusions using warped resolvents and transformed resolvents. The weak, strong, and linear convergence of the proposed algorithms are established under very mild conditions.