A non-monotone smoothing Newton algorithm for solving the system of generalized absolute value equations

TL;DR

This paper introduces a non-monotone smoothing Newton algorithm with line search for solving generalized absolute value equations, demonstrating global and local quadratic convergence under weaker assumptions.

Contribution

It develops a novel smoothing Newton method with non-monotone line search for GAVE, improving convergence properties over existing algorithms.

Findings

Algorithm is globally and locally quadratically convergent.

Numerical results confirm the efficiency and viability of the method.

Abstract

The system of generalized absolute value equations (GAVE) has attracted more and more attention in the optimization community. In this paper, by introducing a smoothing function, we develop a smoothing Newton algorithm with non-monotone line search to solve the GAVE. We show that the non-monotone algorithm is globally and locally quadratically convergent under a weaker assumption than those given in most existing algorithms for solving the GAVE. Numerical results are given to demonstrate the viability and efficiency of the approach.