M-stationarity for a class of MPCCs in Lebesgue spaces

TL;DR

This paper establishes M-stationarity conditions for minimizers of MPCCs in Lebesgue spaces and applies these results to inverse optimal control problems, highlighting the construction of multipliers through convex combinations.

Contribution

It introduces M-stationarity conditions for MPCCs in infinite-dimensional Lebesgue spaces and extends the analysis to inverse optimal control problems.

Findings

M-stationarity conditions hold for minimizers in Lebesgue spaces.

Multipliers can be constructed via convex combinations of auxiliary problem multipliers.

Existence of multipliers is proven only in certain cases.

Abstract

We show that an optimality condition of M-stationarity type holds for minimizers of a class of mathematical programs with complementarity constraints (MPCCs) in Lebesgue spaces. We apply these results also to local minimizers of an inverse optimal control problem (which is an instance of an infinite-dimensional bilevel optimization problem). The multipliers for the M-stationarity system can be constructed via convex combinations of various multipliers to auxiliary, linear problems. However, proving the existence of the multipliers to these auxiliary problems is difficult and only possible in some situations.