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

Authors:
Le Thi Hoai An;Pham Dinh Tao
Affiliations:
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;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
Venue:
Journal of Global Optimization
Year:
1998

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Abstract

In this paper we propose a new branch and bound algorithm using arectangular partition and ellipsoidal technique for minimizing anonconvex quadratic function with box constraints. The boundingprocedures are investigated by d.c. (difference of convex functions)optimization algorithms, called DCA. This is based upon the fact thatthe application of the DCA to the problems of minimizing a quadraticform over an ellipsoid and/or over a box is efficient. Some details ofcomputational aspects of the algorithm are reported. Finally, numericalexperiments on a lot of test problems showing the efficiency of ouralgorithm are presented.