Linearized M-stationarity conditions for general optimization problems

TL;DR

This paper introduces stronger first-order optimality conditions for general optimization problems that are more practical when traditional M-stationarity conditions are difficult to compute, demonstrated through an application to MPEC.

Contribution

It proposes new linearized M-stationarity conditions that improve upon existing conditions for complex optimization problems.

Findings

Stronger optimality conditions are developed for general optimization.

The new conditions are applicable when limiting normal cones are hard to compute.

Application to MPEC shows practical usefulness.

Abstract

This paper investigates new first-order optimality conditions for general optimization problems. These optimality conditions are stronger than the commonly used M-stationarity conditions and are in particular useful when the latter cannot be applied because the underlying limiting normal cone cannot be computed effectively. We apply our optimality conditions to a MPEC to demonstrate their practicability.