EUROPT 2025
Abstract Submission

494. Inner approximations of convex sets and intersections of projectionally exposed cones

Invited abstract in session WB-9: Variational Analysis III, stream Variational analysis: theory and algorithms.

Wednesday, 10:30-12:30
Room: B100/8013

Authors (first author is the speaker)

1. Vera Roshchina
School of Mathematics and Statistics, UNSW Sydney

Abstract

we develop a technique for constructing arbitrarily tight inner convex approximations of compact convex sets with desired facial structure. These inner approximations have the property that all proper faces are extreme points, with the exception of a specific exposed face of the original set. We use this construction to prove that there exists a pair of projectionally exposed cones in dimension 5 whose intersection is not projectionally exposed (providing a negative solution to a couple of conjectures in conic geometry).

The talk is based on joint work with Bruno Lourenço and James Saunderson.

Keywords

Status: accepted


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