A fixed-time stable dynamical model for solving EVLCPs

TL;DR

This paper introduces a fixed-time stable dynamical system for efficiently solving EVLCPs by reformulating them as generalized absolute value equations, providing stability guarantees, solvability conditions, and numerical validation.

Contribution

It develops a novel fixed-time stable dynamical model for EVLCPs based on a new formulation, without smoothing techniques, and introduces new solvability conditions and error bounds.

Findings

Proves fixed-time stability of the proposed dynamical system.

Provides new conditions for the unique solvability of EVLCP.

Demonstrates effectiveness through numerical experiments.

Abstract

A fixed-time stable dynamical system for solving the extended vertical linear complementarity problem (EVLCP) is developed. The system is based on the reformulation of EVLCP as a special case of a new kind of generalized absolute value equations. Some properties of the new kind of generalized absolute value equations are explored which are useful for developing a fixed-time stable dynamical system for solving it. Without using any smoothing technique, we develop a dynamical system for solving the new kind of generalized absolute value equations and prove its fixed-time stability. The model is applicable for solving EVLCP. As two by-products, a new condition which guarantees the unique solvability of EVLCP and a new error bound of EVLCP are given. Numerical results are given to demonstrate our claims.