Potential Theory and Quadratic Programming

TL;DR

This paper extends potential theory concepts to infinite quadratic programming, introducing discretized energy expressions and a method to reduce complex problems to simpler semi-infinite or finite forms using a Chebyshev-constant approach.

Contribution

It develops a novel extension of potential theory to infinite quadratic programming and proposes a discretization method combined with a cutting plane algorithm for problem reduction.

Findings

Extension of potential theory to infinite quadratic programming

Discretized energy expressions similar to Chebyshev constants

Reduction of complex problems to semi-infinite or finite forms

Abstract

We extend the notion of some energy-type expressions based on two sets, developed in the abstract potential theory. We also give the discretized version of the quantities defined, similar to Chebyshev constant. This extension allows to apply the potential-theoretic results to infinite quadratic programming problems. Together with a cutting plane algorithm, the Chebyshev-constant method ensures that under certain conditions, the infinite problem can be reduced to semi-infinite or to finite problems.