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On globally solving linearly constrained indefinite quadratic minimization problems by decomposition branch and bound method

Abstract : The global minimization ofan indefinite quadratic function over a bounded polyhedralset using a décomposition branch and bound approach is considered. The objective functionconsists ofan unseparated convex part and a separated concave part The large-scale problems arecharacterized by hoving the number of convex variables much more thon that of concave variables.The advantages of the method is that it uses the rectangular subdivision on the subspace of concavevariables. Using a easily constmcted convex underestimating function îo the objective function,a lower bound is obtained by solving a convex quadratic programming problem. Three variantsusing exhaustive, adaptive and w-subdivision are discussed. Computational results are presentedfor problems with 10-20 concave variables and up to 200 convex variables.
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https://hal.univ-lorraine.fr/hal-01636785
Contributor : Hoai An Le Thi <>
Submitted on : Thursday, November 16, 2017 - 11:38:24 PM
Last modification on : Wednesday, October 23, 2019 - 10:04:38 AM

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Quynh Phong Thai, Hoai An Le Thi, Tao Pham Dinh. On globally solving linearly constrained indefinite quadratic minimization problems by decomposition branch and bound method. RAIRO - Operations Research, EDP Sciences, 1996, 30 (1), pp.31 - 49. ⟨10.1051/ro/1996300100311⟩. ⟨hal-01636785⟩

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