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A fast and cheap approach for strengthening Lagrangian bound for the generalized Celis-Dennis-Tapia subproblem | ||
| Journal of Mathematical Modeling | ||
| مقالات آماده انتشار، اصلاح شده برای چاپ، انتشار آنلاین از تاریخ 17 آذر 1404 اصل مقاله (299.39 K) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.22124/jmm.2025.31942.2884 | ||
| نویسندگان | ||
| Temadher Alassiry Almaadeed1؛ Abdelouahed Hamdi* 2؛ Akram Taati3 | ||
| 1Qatar University-College of Arts and Sciences-Dept Mathematics and Statistics, P.O. Box 2713 Qatar University, Doha- Qatar | ||
| 2Qatar University-College of Arts and Sciences-Dept Mathematics and Statistics, P.O. Box 2713, Qatar University, Doha- Qatar | ||
| 3Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran. | ||
| چکیده | ||
| In this paper, we consider the generalized Celis-Dennis-Tapia problem which is the problem of minimizing a nonconvex quadratic function subject to two quadratic inequality constraints, one of which being convex. When there is a positive duality gap, by exploiting an equivalent form of the dual Lagrangian problem, we propose to improve the dual bound by adding one or two linear cuts to the Lagrangian relaxation. The present work is motivated by and generalizes the results of [14] for the problem with two strictly convex quadratic constraints. Our main contribution is to show that one can include the feasible region in a con- vex set and then follow the approach in [14] to construct the linear cuts based on supporting hyperplanes of the convex set. Numerical experiments are conducted to assess the quality of the proposed bounds. | ||
| کلیدواژهها | ||
| quadratically constrained quadratic programming؛ Celis-Dennis-Tapia problem؛ dual Lagrangian bound؛ Supporting hyperplane | ||
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