BRANCH AND BOUND METHOD TO RESOLVE NON CONVEX QUADRATIC PROBLEMS OVER A RECTANGLE OF Rⁿ
DOI:
https://doi.org/10.4314/jfas.v11i1.30Keywords:
Global Optimization; Branch and Bound Method; Non convex Quadratic programming; Optimization Methods; Belinear 0-1 programmingAbstract
We present in this paper a new convergence of the Branch and Bound method to resolve a class of non convex quadratic problems over a rectangle of . We construct an approximate convex quadratics functions of the objective function in ordre to determinate the lower bound of the global optimal value of the original problem (NQP) over each subset of the feasible domain of the optimization problem. We applied the partition and reduction technical on the feasable domain t o accelerate the convergence of the proposed algorithm. Finally, we give a simple comparison between this method and another method wish has the same principle with examples.
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References
[1] Gasmi.B, contriution à l'étude des Méthodes de résoluion des problèmes d'optimiations quadratiques. Thèse magister (2007).
[2] G.A. Anastassiou and O. Duman, Intelligent mathematics II, Applied mathematics and approximation theory. Vol 441, DOI 10.10070/978-3-319-30322-2_7, (2016) pp 105-117
[3] Hongwei Jiao, a Branch and Bound algorithm for globally solving a class of non convex programming problems, Non linear analysis 70 (2009) pp 1113-1123
[4] Panos. M. Pardalos, Global optimization algorithms for linearly constrained indefinite quadratic problems, Computers math app lic. Vol. 21, NO 6/7, (1991) pp 87-97.
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[7] Yuelin Gao, Honggang Xue, Peiping Shen, A new rectangle Branch and Bound reduce approch for solving non convex quadratique programming problems, Applied mathemetics and computation 168 (2005), pp 1409-1418.
[2] G.A. Anastassiou and O. Duman, Intelligent mathematics II, Applied mathematics and approximation theory. Vol 441, DOI 10.10070/978-3-319-30322-2_7, (2016) pp 105-117
[3] Hongwei Jiao, a Branch and Bound algorithm for globally solving a class of non convex programming problems, Non linear analysis 70 (2009) pp 1113-1123
[4] Panos. M. Pardalos, Global optimization algorithms for linearly constrained indefinite quadratic problems, Computers math app lic. Vol. 21, NO 6/7, (1991) pp 87-97.
[5] Reiner Horst. Panous. M. Pardalos and Ngugen V. Thoai, Introduction to global optimization. Kluwer academic publishers. Dord Echt/ Boston/ London. Volume 3.(1995).
[6] Xue Honggang, Xu Chengxian, A Branch and Bound algorithm for solving a class of DC-Programming. Applied mathematics and computation 165 ,(2005) pp 291-302 .
[7] Yuelin Gao, Honggang Xue, Peiping Shen, A new rectangle Branch and Bound reduce approch for solving non convex quadratique programming problems, Applied mathemetics and computation 168 (2005), pp 1409-1418.
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Published
2018-12-22
How to Cite
GASMI, B.; BENACER, R. BRANCH AND BOUND METHOD TO RESOLVE NON CONVEX QUADRATIC PROBLEMS OVER A RECTANGLE OF Rⁿ. Journal of Fundamental and Applied Sciences, [S. l.], v. 11, n. 1, p. 469–491, 2018. DOI: 10.4314/jfas.v11i1.30. Disponível em: https://www.jfas.info/index.php/JFAS/article/view/247. Acesso em: 18 oct. 2025.
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