New constraint qualifications for mathematical programs with equilibrium constraints via variational analysis

TL;DR

This paper introduces new constraint qualifications for mathematical programs with equilibrium constraints (MPEC) using variational analysis, providing verifiable conditions that improve upon traditional formulations by avoiding extra multipliers.

Contribution

It proposes novel constraint qualifications for MPEC based on variational analysis, which are weaker and more verifiable than traditional KKT-based conditions.

Findings

Derived verifiable sufficient conditions for metric subregularity.

Established weaker assumptions on problem data.

Linked metric subregularity to calmness of generalized equations.

Abstract

In this paper, we study the mathematical program with equilibrium constraints (MPEC) formulated as a mathematical program with a parametric generalized equation involving the regular normal cone. Compared with the usual way of formulating MPEC through a KKT condition, this formulation has the advantage that it does not involve extra multipliers as new variables, and it usually requires weaker assumptions on the problem data. Using the so-called first order sufficient condition for metric subregularity, we derive verifiable sufficient conditions for the metric subregularity of the involved set-valued mapping, or equivalently the calmness of the perturbed generalized equation mapping.