A numerical method for the solution of relaxed one-sided Lipschitz algebraic inclusions

TL;DR

This paper improves the solvability results for relaxed one-sided Lipschitz algebraic inclusions, enabling a robust numerical method with sharp error estimates, supported by examples and a numerical case study.

Contribution

It introduces an improved solvability theorem that facilitates a new robust numerical method with precise error bounds for algebraic inclusions.

Findings

Enhanced solvability results for algebraic inclusions

Development of a robust numerical approximation method

Provision of sharp error estimates and illustrative examples

Abstract

An existing solvability result for relaxed one-sided Lipschitz algebraic inclusions is substantially improved. This enhanced solvability result allows the design of a very robust numerical method for the approximation of a solution of the algebraic inclusion. Sharp error estimates for this method, illustrative analytic examples and a numerical example are provided.