A branch-and-bound algorithm embedded with DCA for DC programming (Q1954706)

Summary: 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.