Abstract

In this paper, we propose a positive semidefinite relaxation for indefinite quadratic problems with box constraints. We show that a cutting plane procedure can be applied for generating tighter positive semidefinite relaxations. Computational results indicate that the relative gap obtained by the relaxations is less than 1% when the number of variables is up to 100. We also show a branch and bound procedure for obtaining an exact solution of the indefinite problems. Our branching scheme exploits the special structure of box constraints as well as the bounding procedure in which a pair of primal and dual solutions of the associated positive semidefinite relaxation is incorporated.

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