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Nonconvex min-max fractional quadratic problems under quadratic constraints: copositive relaxations. (English) Zbl 1434.90216
Summary: 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.
90C47 Minimax problems in mathematical programming
90C22 Semidefinite programming
90C26 Nonconvex programming, global optimization
90C32 Fractional programming
Full Text: DOI
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