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A Branch and Bound Method via d.c. Optimization Algorithms and Ellipsoidal Technique for Box Constrained Nonconvex Quadratic Problems

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Abstract

In this paper we propose a new branch and bound algorithm using a rectangular partition and ellipsoidal technique for minimizing a nonconvex quadratic function with box constraints. The bounding procedures are investigated by d.c. (difference of convex functions) optimization algorithms, called DCA. This is based upon the fact that the application of the DCA to the problems of minimizing a quadratic form over an ellipsoid and/or over a box is efficient. Some details of computational aspects of the algorithm are reported. Finally, numerical experiments on a lot of test problems showing the efficiency of our algorithm are presented.

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Authors and Affiliations

  1. Mathematical Modelling and Applied Optimization Group, Laboratory of Mathematics, National Institute for Applied Sciences- Rouen, CNRS UPRES-A 60 85, BP 08, F-76131, Mont Saing Aignan, France

    Le Thi Hoai An & Pham Dinh Tao

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  1. Le Thi Hoai An
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  2. Pham Dinh Tao
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An, L.T.H., Tao, P.D. A Branch and Bound Method via d.c. Optimization Algorithms and Ellipsoidal Technique for Box Constrained Nonconvex Quadratic Problems. Journal of Global Optimization 13, 171–206 (1998). https://doi.org/10.1023/A:1008240227198

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