Canonical Solutions to Nonconvex Minimization Problems over Lorentz Cone

TL;DR

This paper introduces a canonical duality approach to efficiently solve nonconvex quadratic minimization problems over Lorentz cones, transforming them into convex dual problems with clear extremality conditions.

Contribution

It develops a novel canonical dual framework for nonconvex Lorentz cone problems, enabling solution via standard convex optimization techniques.

Findings

Transform nonconvex problems into convex dual problems

Classify extremality conditions using triality theory

Demonstrate applications of the method

Abstract

This paper presents a canonical dual approach for solving nonconvex quadratic minimization problem. By using the canonical duality theory, nonconvex primal minimization problems over n-dimensional Lorentz cone can be transformed into certain canonical dual problems with only one dual variable, which can be solved by using standard convex minimization methods. Extremality conditions of these solutions are classified by the triality theory. Applications are illustrated.