A Newton-Fixed Point Homotopy Algorithm For Nonlinear Complementarity Problems With Generalized Monotonicity

TL;DR

This paper introduces a probability-one homotopy algorithm for solving nonlinear complementarity problems with generalized monotonicity, providing theoretical convergence guarantees and promising preliminary numerical results.

Contribution

It proposes a new Newton-Fixed Point Homotopy algorithm with proven global convergence for generalized monotone NCPs, advancing computational methods for nonlinear systems.

Findings

Algorithm demonstrates probability-one convergence

Preliminary experiments show effectiveness on difficult problems

Provides a theoretical foundation for new computational approaches

Abstract

In this paper has been considered probability-one global convergence of NFPH (Newton-Fixed Point Homotopy) algorithm for system of nonlinear equations and has been proposed a probability-one homotopy algorithm to solve a regularized smoothing equation for NCP with generalized monotonicity. Our results provide a theoretical basis to develop a new computational method for nonlinear equation systems and complementarity problems. Some preliminary numerical experiments shows that our NFPH method is useful and promissing for difficult nonlinear problems.