A continuous GRASP for global optimization with general linear constraints
João Lauro FACO

07 September 2012, 10h30 Salle/Bat : 475/PCRI-N
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Résumé :

A new variant of the global optimization method Continuous GRASP (C-GRASP) is presented. The new variant incorporates general linear constraints in addition to box constraints. C-GRASP solves continuous
global optimization problems subject to box constraints by adapting the greedy randomized adaptive search procedure (GRASP) of Feo and Resende (1989) for discrete optimization. It has been applied to a wide range of continuous optimization problems. We consider the box constraints as implicit and handle the general linear equality/inequality constraints explicitly. If we are given an m x n matrix A, with m ≤ n, then m basic variables can be eliminated from the global optimization problem. A Reduced Problem in (n-m) independent variables will be subject only to the box constraints. The C-GRASP solver is a derivative-free global optimization method yielding an optimal or near-optimal solution to the Reduced Problem. The basic variables can be computed by solving a system of linear equations. If all basic variables are inside the box, the algorithm stops. Otherwise a change-of-basis procedure is applied, and a new Reduced Problem is solved.