Global Escape Strategies for Maximizing Quadratic Forms over a Simplex

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.