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

Abstract: 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: , with , we can show the proposed algorithm solves problems of the form in polynomial time when the rank of the matrix is fixed and the number of its positive diagonal entries is . [Copyright &y& Elsevier]