# New sharp necessary optimality conditions for mathematical programs with equilibrium constraints

## TL;DR

This paper introduces a new, sharper necessary optimality condition for mathematical programs with equilibrium constraints, applicable even without constraint qualifications, improving upon existing M-stationary conditions.

## Contribution

It develops a novel necessary optimality condition for MPECs that surpasses traditional conditions and remains valid without constraint qualifications.

## Key findings

- New necessary optimality condition derived
- Condition sharper than M-stationary
- Applicable without constraint qualifications

## 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. We derive a new necessary optimality condition which is sharper than the usual M-stationary condition and is applicable even when no constraint qualifications hold for the corresponding mathematical program with complementarity constraints (MPCC) reformulation.