A Branch-and-Bound Algorithm Embedded with DCA for DC Programming. (12th July 2012)

• Record Type: Journal Article
• Authors: Wang, Meihua; Xu, Fengmin; Xu, Chengxian
• Other Names: Liu Wanquan Academic Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2012(2012)
• Publication Date: 2012-07-12
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2012/364607
• Languages: English
• ISSNs: 1024-123X

Abstract

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.