Non-convex min-max fractional quadratic problems under quadratic constraints: copositive relaxations

Paula A. Amaral (pacafct.unl.pt)
Immanuel M. Bomze (immanuel.bomzeunivie.ac.at)

Abstract: In this paper we address a min-max problem of fractional quadratic (not necessarily convex) over linear functions on a feasible set described by linear and (not necessarily convex) quadratic functions. We propose a conic reformulation on the cone of completely positive matrices. By relaxation, a doubly non negative conic formulation is used to provide lower bounds with evidence of very small gaps. It is known that in many solvers using Branch and Bound the optimal solution is obtain in early stages and a heavy computational price is payed in the next iterations to obtain the optimality certificate. To reduce this effort tight lower bounds are crucial. We will show empirical evidence that lower bounds provided by the copositive relaxation is able to substantially speed up a well known solver in obtaining the optimality certificate.

Keywords: Min-max fractional quadratic problems, conic reformulations, copositive cone, completly positive cone, lower bounds

Category 1: Linear, Cone and Semidefinite Programming

Category 2: Nonlinear Optimization (Quadratic Programming )

Citation: Accepted for publication

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Entry Submitted: 10/09/2018
Entry Accepted: 10/16/2018
Entry Last Modified: 05/08/2019

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