Explicit criterion of uniform LP duality for linear problems of copositive optimization

TL;DR

This paper establishes new necessary and sufficient conditions for uniform LP duality in copositive optimization, enhancing understanding of duality properties in conic matrix systems.

Contribution

It introduces novel criteria for uniform LP duality in copositive programming, formulated through equivalent conditions using immobile indices.

Findings

New necessary and sufficient conditions for uniform LP duality.

Equivalent formulations of duality conditions using immobile indices.

Enhanced theoretical understanding of duality in copositive optimization.

Abstract

An uniform LP duality is an useful property of conic matrix systems. A consistent linear conic optimization problem yields uniform LP duality if for any linear cost function, for which the primal problem has finite optimal value, the corresponding Lagrange dual problem is attainable and the duality gap vanishes. In this paper, we establish new necessary and sufficient conditions guaranteing the uniform LP duality for linear problems of Copositive Programming and formulate these conditions in different equivalent forms. The main results are obtained using an approach developed in previous papers of the authors and based on a concept of immobile indices that permits alternative representations of the set of feasible solutions.