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A clique algorithm for standard quadratic programming. (English) Zbl 1163.90691
Summary: 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.

90C20 Quadratic programming
05C35 Extremal problems in graph theory
05C85 Graph algorithms (graph-theoretic aspects)
Full Text: DOI
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