Maximally Monotone Linear Subspace Extensions of Monotone Subspaces: Explicit Constructions and Characterizations

TL;DR

This paper provides explicit constructions and characterizations of maximally monotone linear subspace extensions of monotone linear relations in finite-dimensional spaces, generalizing recent results and illustrating with examples.

Contribution

It introduces explicit methods for extending monotone linear relations to maximal monotonicity, broadening understanding in finite-dimensional spaces.

Findings

Explicit constructions of maximal monotone extensions

Generalization of recent theoretical results

Illustrative examples demonstrating the extensions

Abstract

Monotone linear relations play important roles in variational inequality problems and quadratic optimizations. In this paper, we give explicit maximally monotone linear subspace extensions of a monotone linear relation in finite dimensional spaces. Examples are provided to illustrate our extensions. Our results generalize a recent result by Crouzeix and Anaya.