Le Thi H.A.,CNRS Theoretical and Applied Informatics |
Dinh T.P.,Bp08 Avenue Of Luniversite |
Van Ngai H.,University of Quynhon
Journal of Global Optimization | Year: 2012
In the present paper, we are concerned with conditions ensuring the exact penalty for nonconvex programming. Firstly, we consider problems with concave objective and constraints. Secondly, we establish various results on error bounds for systems of DC inequalities and exact penalty, with/without error bounds, in DC programming. They permit to recast several class of difficult nonconvex programs into suitable DC programs to be tackled by the efficient DCA. © Springer Science+Business Media, LLC. 2011.
Pham Dinh T.,Bp08 Avenue Of Luniversite |
Nguyen Canh N.,Bp08 Avenue Of Luniversite |
Le Thi H.A.,University of Lorraine
Journal of Global Optimization | Year: 2010
This paper addresses a new continuous approach based on the DC (Difference of Convex functions) programming and DC algorithms (DCA) to Binary quadratic programs (BQP) which play a key role in combinatorial optimization. DCA is completely different from other avalaible methods and featured by generating a convergent finite sequence of feasible binary solutions (obtained by solving linear programs with the same constraint set) with decreasing objective values. DCA is quite simple and inexpensive to handle large-scale problems. In particular DCA is explicit, requiring only matrix-vector products for Unconstrained Binary quadratic programs (UBQP), and can then exploit sparsity in the large-scale setting. To check globality of solutions computed by DCA, we introduce its combination with a customized Branch-and-Bound scheme using DC/SDP relaxation. The combined algorithm allows checking globality of solutions computed by DCA and restarting it if necessary and consequently accelerates the B&B approach. Numerical results on several series test problems provided in OR-Library (Beasley in J Global Optim, 8:429-433, 1996), show the robustness and efficiency of our algorithm with respect to standard methods. In particular DCA provides ε-optimal solutions in almost all cases after only one restarting and the combined DCA-B&B-SDP always provides (ε-)optimal solutions. © 2010 Springer Science+Business Media, LLC.