Nonconvex min–max fractional quadratic problems under quadratic constraints

Author(s)
Paula Alexandra Amaral, Immanuel M. Bomze
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 nonnegative 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 obtained in early stages and a heavy computational price is paid 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 are able to substantially speed up a well known solver in obtaining the optimality certificate.

Organisation(s)
Department of Statistics and Operations Research, Research Platform Data Science @ Uni Vienna
Journal
Journal of Global Optimization
ISSN
0925-5001
DOI
https://doi.org/10.1007/s10898-019-00780-3
Publication date
05-2019
Publication status
E-pub ahead of print
Peer reviewed
Yes
Austrian Fields of Science 2012
101015 Operations research
Keywords
Completely positive cone, Conic reformulations, Copositive cone, Lower bounds, Min–max fractional quadratic problems, ISOR, CSP, MR
ASJC Scopus subject areas
Computer Science Applications, Control and Optimization, Management Science and Operations Research, Applied Mathematics
Portal url
https://ucris.univie.ac.at/portal/en/publications/nonconvex-minmax-fractional-quadratic-problems-under-quadratic-constraints(81a73a8a-ad6c-4d69-911f-d93a62db2277).html