Maximizing The Distance To A "Far Enough" Point Over The Intersection Of Hyper-Disks

TL;DR

This paper introduces a new feasibility criterion for intersecting convex sets and extends it to a non-convex case involving hyper-disks, providing efficient methods to verify set inclusion.

Contribution

It proposes a novel convex feasibility criterion and extends it to hyper-disk intersections, offering practical algorithms for set inclusion verification.

Findings

Feasibility criterion simplifies intersection analysis

Algorithm effectively verifies hyper-disk inclusion

Applicable to convex and certain non-convex set intersections

Abstract

We present a novel feasibility criteria for the finite intersection of convex sets given by inequalities. This criteria allows us to easily assert the feasibility by analyzing the unconstrained minimum of a speci?fic convex function, that we form with the given sets. Next an algorithm is presented which extends the idea to a particular non-convex case: assert the inclusion of the fi?nite intersection of a set of hyper-disks with equal radii in another hyper-disk with a different radius.