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
External organisation(s)
Universidade Nova de Lisboa
Journal
Journal of Global Optimization
Volume
75
Pages
227–245
ISSN
0925-5001
DOI
https://doi.org/10.1007/s10898-019-00780-3
Publication date
05-2019
Peer reviewed
Yes
Austrian Fields of Science 2012
Operations research
Keywords
ASJC Scopus subject areas
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Portal url
https://ucris.univie.ac.at/portal/en/publications/nonconvex-minmax-fractional-quadratic-problems-under-quadratic-constraints(81a73a8a-ad6c-4d69-911f-d93a62db2277).html