A parallel algorithm for constrained concave quadratic global minimization
Mathematical Programming: Series A and B
Annals of Operations Research - Special issue on Tabu search
A Deterministic Approach to Linear Programs with Several Additional Multiplicative Constraints
Computational Optimization and Applications
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In this paper, we will propose an efficient heuristic algorithm forsolving concave quadratic programming problems whose rank of the objectivefunction is relatively small. This algorithm is a combination of Tuy‘scutting plane to eliminate the feasible region and a kind of tabu-searchmethod to find a ’good‘ vertex. We first generate a set of V of vertices andselect one of these vertices as a starting point at each step, and applytabu-search and Tuy‘s cutting plane algorithm where the list of tabuconsists of those vertices eliminated by cutting planes and those newlygenerated vertices by cutting planes. When all vertices of the set V areeliminated, the algorithm is terminated. This algorithm need not converge toa global minimum, but it can work very well when the rank is relativelysmall (up to seven). The incumbent solutions are in fact globally optimalfor all tested problems. We also propose an alternative algorithm byincorporating Rosen‘s hyperrectangle cut. This algorithm is more efficientthan the combination of Tuy‘s cutting plane and tabu-search.