Strong Duality in Nonconvex Quadratic Problems with Separable Quadratic Constraints

TL;DR

This paper establishes conditions under which nonconvex quadratic problems with separable quadratic constraints exhibit strong duality, introduces a distributed solution algorithm, and demonstrates these results on robust least squares problems.

Contribution

It provides new sufficient conditions for strong duality in nonconvex quadratic problems with separable constraints and proposes a distributed algorithm for their optimal solution.

Findings

Strong duality holds under derived conditions.

Distributed algorithm achieves optimal solutions.

Robust least squares problem satisfies strong duality.

Abstract

We study nonconvex quadratic problems (QPs) with quadratic separable constraints, where these constraints can be defined both as inequalities or equalities. We derive sufficient conditions for these types of problems to present the S-property, which ultimately guarantees strong duality between the primal and dual problems of the QP. We study the existence of solutions and propose a novel distributed algorithm to solve the problem optimally when the S-property is satisfied. Finally, we illustrate our theoretical results proving that the robust least squares problem with multiple constraints has the strong duality property.