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Journal of Applied Mathematics
Volume 2013 (2013), Article ID 215312, 9 pages
http://dx.doi.org/10.1155/2013/215312
Research Article

A Global Optimization Algorithm for Generalized Quadratic Programming

1Department of Mathematics, Henan Institute of Science and Technology, Xinxiang 453003, China
2Department of Mathematics, Xidian University, Xi'an 710071, China
3Department of Mathematics, Henan Normal University, Xinxiang 453007, China

Received 13 June 2013; Accepted 13 August 2013

Academic Editor: Md Sazzad Chowdhury

Copyright © 2013 Hongwei Jiao and Yongqiang Chen. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We present a global optimization algorithm for solving generalized quadratic programming (GQP), that is, nonconvex quadratic programming with nonconvex quadratic constraints. By utilizing a new linearizing technique, the initial nonconvex programming problem (GQP) is reduced to a sequence of relaxation linear programming problems. To improve the computational efficiency of the algorithm, a range reduction technique is employed in the branch and bound procedure. The proposed algorithm is convergent to the global minimum of the (GQP) by means of the subsequent solutions of a series of relaxation linear programming problems. Finally, numerical results show the robustness and effectiveness of the proposed algorithm.