Extremality of Convex Sets with Some Applications

TL;DR

This paper introduces an advanced concept of extremality for convex sets in topological vector spaces, providing new conditions and applications in normal cone calculus and support function convolutions.

Contribution

It develops an enhanced extremality notion and derives novel calculus rules for convex set intersections and support functions.

Findings

New extremality conditions for convex sets in topological vector spaces

Improved intersection rules for normal cones

Enhanced calculus for infimal convolutions of support functions

Abstract

In this paper we introduce an enhanced notion of extremal systems for sets in locally convex topological vector spaces and obtain efficient conditions for set extremality in the convex case. Then we apply this machinery to deriving new calculus results on intersection rules for normal cones to convex sets and on infimal convolutions of support functions.