Nonmonotone Spectral Analysis for Variational Inclusions

TL;DR

This paper introduces a spectral subgradient algorithm with nonmonotone line search for variational inclusion problems, enhancing convergence and ability to escape local minima in non-convex optimization.

Contribution

It combines spectral eigenvalue-based acceleration with nonmonotone strategies, providing a novel approach for global convergence in variational inclusions.

Findings

Accelerates convergence using spectral properties.

Effectively escapes local minima with nonmonotone strategies.

Ensures global convergence of the proposed algorithm.

Abstract

Gradient descent algorithms perform well in convex optimization but can get tied for finding local minima in non-convex optimization. A robust method that combines a spectral approach with nonmonotone line search strategy for solving variational inclusion problems is proposed. Spectral properties using eigenvalues information are used for accelerating the convergence. Nonmonotonic behaviour is exhibited to relax descent property and escape local minima. Nonmonotone spectral conditions leverage adaptive search directions and global convergence for the proposed spectral subgradient algorithm.