Lipschitz and H\"older stability of optimization problems and generalized equations

TL;DR

This paper investigates the stability of solutions to parametric optimization problems and generalized equations with disjunctive constraints, providing conditions for Lipschitz and H"older continuity and improving classical results in nonlinear programming.

Contribution

It introduces new sufficient conditions for stability of solutions under constraint qualifications, extending and enhancing existing stability results in optimization theory.

Findings

Established conditions for Lipschitz and H"older stability

Applied results to parametric mathematical programs with equilibrium constraints

Improved classical stability results in nonlinear programming

Abstract

This paper studies stability aspects of solutions of parametric mathematical programs and generalized equations, respectively, with disjunctive constraints. We present sufficient conditions that, under some constraint qualifications ensuring metric subregularity of the constraint mapping, continuity results of upper Lipschitz and upper H\"older type, respectively, hold. Furthermore, we apply the above results to parametric mathematical programs with equilibrium constraints and demonstrate, how some classical results for the nonlinear programming problem can be recovered and even improved by our theory.