Maximization of a Convex Quadratic Function Under Linear Constraints

Konno, H. (1975). Maximization of a Convex Quadratic Function Under Linear Constraints. IIASA Research Memorandum. IIASA, Laxenburg, Austria: RM-75-060

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Abstract

This paper addresses the maximization of a convex quadratic function subject to linear constraints. We first prove the equivalence of this problem to the associated bilinear program. Next we apply a theory of bilinear programming to compute a local maximum and to generate a cutting plane which eliminates a region containing that local maximum. Then we develop an iterative procedure to improve a given cut by exploiting the symmetric structure of the bilinear program. This procedure either generates a point which is strictly better than the best local maximum found, or generates a cut which is deeper (usually much deeper) than Tui's cut. Finally the results of numerical experiments on small problems are reported.

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