Abstract
We consider the problem of minimizing a quadratic function with a knapsack constraint. Quadratic knapsack problems have numerous applications, including the least distance problem, quadratic programming defined on the convex hull of a set of points, and the maximum clique problem. We propose and analyze three algorithms for solving quadratic knapsack problems. Two algorithms are based on recently developed interior point methods. The first solves convex quadratic problems, and the second computes a stationary point for the indefinite case. For both, computational results on a variety of test problems are presented. The third algorithm, based on simplicial partitioning and convex underestimating functions, can be used to compute the global optimum of indefinite quadratic knapsack problems.
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