Polyhedrality,Complementarity and Regularity with Applications to Variational Inequalities over Polyhedral Sets

TL;DR

This paper introduces a new geometric approach to variational inequalities over polyhedral sets, simplifying proofs and extending classical regularity results using elementary convex geometry and metric regularity theory.

Contribution

It develops a novel approach that generalizes existing regularity results for variational inequalities over polyhedral sets without relying on advanced variational analysis techniques.

Findings

New geometric method for variational inequalities

Generalizations of classical regularity results

Simplified proofs using elementary convex geometry

Abstract

The regularity theory for variational inequalities over polyhedral sets developed in a series of papers by Robinson, Ralph and Dontchev-Rockafellar in the 90s has long become classics of variational analysis. But in the available proofs of almost all main results, fairly nontrivial as they are, techniques of variational analysis do not play a significant part. In the paper we develop a new approach that allows to obtain some generalizations of the the mentioned results without invoking anything beyond elementary geometry of convex polyhedra and some basic facts of the theory of metric regularity.