On the Relation Between Affinely Adjustable Robust Linear Complementarity and Mixed-Integer Linear Feasibility Problems

TL;DR

This paper explores the connection between affinely adjustable robust linear complementarity problems and mixed-integer linear feasibility problems, extending previous results to convex uncertainty sets and establishing computational equivalences.

Contribution

It extends prior work to convex and compact uncertainty sets and proves equivalence between adjustable robust solutions and mixed-integer feasibility for polyhedral sets.

Findings

Extension to convex and compact uncertainty sets.

Equivalence between robust solutions and mixed-integer feasibility for polyhedral sets.

Provides theoretical foundations for computational approaches.

Abstract

We consider adjustable robust linear complementarity problems and extend the results of Biefel et al. (2022) towards convex and compact uncertainty sets. Moreover, for the case of polyhedral uncertainty sets, we prove that computing an adjustable robust solution of a given linear complementarity problem is equivalent to solving a properly chosen mixed-integer linear feasibility problem.