Mathematical Problems in Engineering
Volume 2012, Article ID 364607, 16 pages
http://dx.doi.org/10.1155/2012/364607
A Branch-and-Bound Algorithm Embedded with DCA for DC Programming
1Department of Mathematics, Xi'an Jiaotong University, Xi'an 710049, China
2SKLMSE Laboratory and Department of Mathematics, Xi'an Jiaotong University, Xi'an 710049, China
Received 10 October 2011; Revised 16 March 2012; Accepted 17 March 2012
Academic Editor: Wanquan Liu
Copyright © 2012 Meihua Wang et al. 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
The special importance of Difference of Convex (DC) functions programming has been recognized in recent studies on nonconvex optimization problems. In this work, a class of DC programming derived from the portfolio selection problems is studied. The most popular method applied to solve the problem is the Branch-and-Bound (B&B) algorithm. However, “the curse of dimensionality” will affect the performance of the B&B algorithm. DC Algorithm (DCA) is an efficient method to get a local optimal solution. It has been applied to many practical problems, especially for large-scale problems. A B&B-DCA algorithm is proposed by embedding DCA into the B&B algorithms, the new algorithm improves the computational performance and obtains a global optimal solution. Computational results show that the proposed B&B-DCA algorithm has the superiority of the branch number and computational time than general B&B. The nice features of DCA (inexpensiveness, reliability, robustness, globality of computed solutions, etc.) provide crucial support to the combined B&B-DCA for accelerating the convergence of B&B.