Global Escape Strategies for Maximizing QuadraticForms over a Simplex

Authors:
Immanuel M. Bomze
Affiliations:
Department of Statistics, Operations Research and Computer Science, University of Vienna, Vienna, Austria
Venue:
Journal of Global Optimization
Year:
1997

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Abstract

Consider the problem of maximizing a quadratic formover the standard simplex.Problems of this type occur, e.g., in the search for the maximum (weighted)clique in an undirected graph.In this paper, copositivity-based escape proceduresfrom inefficient local solutions are rephrased into lower-dimensionalsubproblems which are again of the same type. As a result, analgorithm is obtained which tries to exploit favourable data constellationsin a systematic way, and to avoid the worst-case behaviourof such NP-hard problems whenever possible. First results onfinding large cliques in DIMACS benchmark graphs are encouraging.