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G-2011-01

A simple finite simplicial covering algorithm for concave minimization over a polytope

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We propose a conceptually simple, finite simplicial branch-and-bound algorithm for minimizing a concave function over a polytope. The proposed algorithm requires at each iteration the solution of two closely related linear programs of constant size for the computation of the lower bound and of the subdivision point; moreover, the objective function need to be evaluated only at extreme points of the polytope and of the initial simplex. Preliminary computational results are presented, which point to future improvements.

, 16 pages

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