A branch-and-bound algorithm embedded with DCA for DC programming

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 (BB) algorithm. However, the curse of dimensionality will affect the performance of the BB 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 BB-DCA algorithm is proposed by embedding DCA into the BB algorithms, the new algorithm improves the computational performance and obtains a global optimal solution. Computational results show that the proposed BB-DCA algorithm has the superiority of the branch number and computational time than general BB. The nice features of DCA (inexpensiveness, reliability, robustness, globality of computed solutions, etc.) provide crucial support to the combined BB-DCA for accelerating the convergence of BB. © 2012 Meihua Wang et al.