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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.

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