Nonconvex min–max fractional quadratic problems under quadratic constraints: copositive relaxations

Paula Alexandra Amaral () and Immanuel M. Bomze ()
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Paula Alexandra Amaral: Universidade Nova de Lisboa
Immanuel M. Bomze: Universität Wien

Journal of Global Optimization, 2019, vol. 75, issue 2, No 1, 227-245

Abstract: 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.

Keywords: Min–max fractional quadratic problems; Conic reformulations; Copositive cone; Completely positive cone; Lower bounds; 90C47; 90C22; 90C26; 90C32 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10898-019-00780-3

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