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We study approaches for obtaining convex relaxations of global optimization problems containing multilinear functions. Specifically, we compare the concave and convex envelopes of these functions with the relaxations that are obtained with a standard relaxation approach, due to McCormick. The standard approach reformulates the problem to contain only(More)
We study the convex hull of the bounded, nonconvex set M n = { n + 1} for any n ≥ 2. We seek to derive strong valid linear inequalities for M n ; this is motivated by the fact that many exact solvers for nonconvex problems use polyhedral relaxations so as to compute a lower bound via linear programming solvers. We present a class of linear inequalities(More)
Pivot-and-Fix, a new primal heuristic for finding feasible solutions for mixed integer programming (MIP) problems is presented in this paper. Pivot-and-Fixtries to explore potentially promising extreme points of the polyhedron of the problem and by forming smaller serach trees looks for integer feasible solutions. Computational results show that this(More)
In this paper we are about to modify the fuzzy c-mean (FCM) algorithm in a way which this algorithm be able to handle the cases in which the data set is multidimensional, and dimensions are not of equal degree of importance. In such cases, clusters obtained by FCM are not logically satisfying. So some modifications are absolutely needed.
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