A dynamical system based on projection operator for solving absolute value equations associated with second-order cone

TL;DR

This paper introduces a dynamical system approach based on projection operators to solve second-order cone absolute value equations, demonstrating stability and effectiveness through numerical simulations.

Contribution

It presents a novel dynamical system formulation for SOCAVEs and proves conditions for stability, with numerical validation of the method's effectiveness.

Findings

Equilibrium points exist and are globally asymptotically stable under certain conditions.

Numerical simulations confirm the method's effectiveness.

The approach provides a new tool for solving SOCAVEs efficiently.

Abstract

A new equivalent reformulation of the absolute value equations associated with second-order cone (SOCAVEs) is emphasised, from which a dynamical system based on projection operator for solving SOCAVEs is constructed. Under proper assumptions, the equilibrium points of the dynamical system exist and could be (globally) asymptotically stable. Some numerical simulations are given to show the effectiveness of the proposed method.