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Article Dans Une Revue Discrete Applied Mathematics Année : 2011

A polynomial-time recursive algorithm for some unconstrained quadratic optimization problems

Résumé

Determining the cells of an arrangement of hyperplanes is a classical problem in combinatorial geometry. In this paper we present an efficient recursive procedure to solve it. In fact, by considering a connection between the latter problem and optimality conditions of unconstrained quadratic optimization problems in the following form: (QP) min{xQx | x in {-1,1}n}, with Q in Rn×n, we can show the proposed algorithm solves problems of the form (QP) in polynomial time when the rank of the matrix Q is fixed and the number of its positive diagonal entries is O(log(n)).

Dates et versions

hal-00679017 , version 1 (14-03-2012)

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Walid Ben-Ameur, José Neto. A polynomial-time recursive algorithm for some unconstrained quadratic optimization problems. Discrete Applied Mathematics, 2011, 159 (16), pp.1689-1698. ⟨10.1016/j.dam.2010.08.028⟩. ⟨hal-00679017⟩
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