A class of matrix splitting-based fixed-point iteration method for the vertical nonlinear complementarity problem

TL;DR

This paper introduces a new class of fixed-point iteration methods based on matrix splitting for solving the vertical nonlinear complementarity problem, demonstrating improved efficiency through theoretical convergence analysis and numerical experiments.

Contribution

The paper proposes a novel matrix splitting-based fixed-point iteration method for VNCP and provides convergence analysis and efficiency comparisons.

Findings

FPI method converges under certain conditions

FPI outperforms existing methods in computational efficiency

Estimated iteration counts demonstrate practical effectiveness

Abstract

In this paper, we propose a class of matrix splitting-based fixed-point iteration (FPI) methods for solving the vertical nonlinear complementarity problem (VNCP). Under appropriate conditions, we present two convergence results obtained using different techniques and estimate the number of iterations required for the FPI method. Additionally, through numerical experiments, we demonstrated that the FPI method surpasses other methods in computational efficiency.