Optimality Conditions And Algorithms For DC Programming

DC programming has an important position in the field of non-convex programming, and it is very popular in recent years because of its special structures and wide range of application background. In the field of global optimization, many effective algorithms are based on DC programming, and there are a large class of functions can be seen as DC functions. The algorithms for solving DC programming are divided into combination algorithm and convex analysis algorithm. All of these algorithms can only obtain the local optimal solution of the objective function. For getting the global optimal solution of DC programming quickly and efficiently, we can combine the above two types of algorithm. Optimality conditions and algorithms of DC programming are studied in this paper. First of all, we introduce the concept of DC programming, commonly used algorithm for global optimization problems and research background in chapter one. Then, in the second chapter, we focus on the optimality conditions of DC programming. The necessary and sufficient condition of global optimal solution for a special class of unconstrained DC programming is found by using the properties of convex function. DCA algorithm is used for solving a class of DC programming with convex constraints in chapter three, and this DC programming is converted into unconstrained DC programming by using the properties of indicator function and penalty function. In the last chapter of this paper, the branch and bound algorithm of DC programming is studied. We give a branch and bound algorithm for solving DC programming and prove the convergence of the algorithm.