University of Guilan Journal of Mathematical Modeling 2345-394X 14 2 2026 05 01 A fast and cheap approach for strengthening Lagrangian bound for the generalized Celis-Dennis-Tapia subproblem 595 608 9264 10.22124/jmm.2025.31942.2884 EN Temadher Alassiry Almaadeed Qatar University-College of Arts and Sciences-Dept Mathematics and Statistics, P.O. Box 2713 Qatar University, Doha- Qatar Abdelouahed Hamdi Qatar University-College of Arts and Sciences-Dept Mathematics and Statistics, P.O. Box 2713, Qatar University, Doha- Qatar Akram Taati Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran. Journal Article 2025 10 11 In this paper, we consider the generalized Celis-Dennis-Tapia problem<br />which is the problem of minimizing a nonconvex quadratic function subject to<br />two quadratic inequality constraints, one of which being convex. When there is<br />a positive duality gap, by exploiting an equivalent form of the dual Lagrangian<br />problem, we propose to improve the dual bound by adding one or two linear cuts<br />to the Lagrangian relaxation. The present work is motivated by and generalizes<br />the results of [14] for the problem with two strictly convex quadratic constraints.<br />Our main contribution is to show that one can include the feasible region in a con-<br />vex set and then follow the approach in [14] to construct the linear cuts based on<br />supporting hyperplanes of the convex set. Numerical experiments are conducted<br />to assess the quality of the proposed bounds. https://jmm.guilan.ac.ir/article_9264_3bb0c7a429b19885a3efa780276fd8df.pdf