DC Programming Algorithm And Its Convergence

DC programming is a more general form of convex programming. DC programming plays aninteresting and important part because of its theoretical aspects as well as its wide range ofapplications in Economy, Engineering and Computational Mathematics. The theory of DCprogramming (including convex programming) and its algorithm research are of great significance. Inthis article, we have a good research on the algorithm of DC programming and convex programming.And we have analyzed convergence of the algorithm.In the chapter two of the article, we gave out more than the equivalent of optimality conditions ofthe convex programming with constraints. Proximal point algorithm, which is used to treating convexprogramming without constraints, is now generalized to solve convex programming with constraints.Therefore，the proximal point algorithm of the convex programming with constraints is given. Thegeneralized one is proved to be both descent and convergent in a simple and clear way.In2003, proximal point algorithm, which is used to treating convex programming withoutconstraints, is generalized to solve DC programming without constraints by Wenyu Sun. Therefore,the proximal point algorithm is given. In the chapter three of the article, proximal point algorithm,which is used to treating convex programming with constraints, is now generalized to solve DCprogramming with constraints. Then，the proximal point algorithm is given. The generalized one isproved to be both descent and convergent in a simple and clear way. It’s worth pointing out that in theprocess of proofing and it’s only used the property of subdifferential as a tool.