The Proximal Point Algorithm And The Global Algorithm For DC Programming

In the field of nonconvex optimization, DC programming plays an interesting and important part because of its theoretical aspects as well as its wide range of applications in economy and engineering. In the chapter two of the paper proximal point algorithm, which is used to treating convex programming without constraints, is now generalized to solve convex programming and DC programming with constraints. Then,theε? proximal point algorithm is given. The generalized one is proved to be both descent and convergent in a simple and clear way. It's worth pointing out that in the proof process it's only used the property of subdifferential as a tool. In the chapter three of the paper different global convergent algorithms are provided for DC programmings with different constraints correspondingly. When the objective function is the sum of a convex functions and a separate concave function, and the constraints are the intersection of a polytop and a rectangular, a branch and bound algorithm with a normal rectangular subdivision is given. When the DC programming has an additional reverse convex constraint, using a related exact penalty, then we solve it by the combined DCA—branch and bound algorithm. The two algorithms have been proved to be right and efficient both in theory and numerical experiments.