The Global And The Proximal Point Algorithm For Solving DC Programming

It is well known that DC programming is an important nonlinear programming.Now more and more attention have been paid on it because of its broad implication ineconomy and engineering. In the chapter two of the paper we combined DCA withBranch and Bound algorithm, one new algorithm was given. And both in theory andnumerical example the new algorithm has been proved to be right and efficient. Asthe implication the new algorithm can be used to solve the undefinited quadraticprogramming and the generalized geometry programming. On the other hand, thereason why the DC programming is paid so much attention isbecause of its nonsmooth. In the charpter three of the paper, one modified proximalpoint algorithm , using Bregman function for solving DC programming, that is basedon the one proposed by Sun.The algorithm is proved to be both descent andconvergent. Furthermore the algorithm can not only be applied to solve theunconstrained DC programming,but the convex constrained one when the Bregmanfunction is Boundary Coercive. When the initial point chosen lied in the interior ofthe constrained set,it can be proved that the sequence got from the algorithm totallybelong to the constrained set. So the algorithm can also be said to be one interiorpoint algorithm. In the last, one modified proximal algorithm for solving convexprogramming is modified in technique and the convergence and convergent speed ofthe new algorithm is provided.