A clique algorithm for standard quadratic programming

Authors:
Andrea Scozzari;Fabio Tardella
Affiliations:
Universití di Roma "La Sapienza", Dip. di Matematica per le Decisioni Economiche, Finanziarie ed Assicurative, Roma, Italy;Universití di Roma "La Sapienza", Dip. di Matematica per le Decisioni Economiche, Finanziarie ed Assicurative, Roma, Italy
Venue:
Discrete Applied Mathematics
Year:
2008

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Abstract

A standard Quadratic Programming problem (StQP) consists in minimizing a (nonconvex) quadratic form over the standard simplex. For solving a StQP we present an exact and a heuristic algorithm, that are based on new theoretical results for quadratic and convex optimization problems. With these results a StQP is reduced to a constrained nonlinear minimum weight clique problem in an associated graph. Such a clique problem, which does not seem to have been studied before, is then solved with an exact and a heuristic algorithm. Some computational experience shows that our algorithms are able to solve StQP problems of at least one order of magnitude larger than those reported in the literature.