Research On Semi-Infinite Programming

The paper consists of three parts: in the first chapter, we briefly give a review on the origin, applications, development of semi-infinite programming, also the developing situation of it is presented. Then we propose the problems that will be discussed in the following papers. Also, we introduce the theory in the field of feasible region for semi-infinite programming, and concluded that in some area around the feasible points, feasible region can be expressed by finite inequality constraints, this results gives a base to the following algorithms. By combining analysis center cutting plane methods which have developed fast in the last years, we get a analysis center cutting plane methods for convex semi-infinite programming, which has a good convergence under modest assumptions. In chapter 3, we give an equivalent form of semi-infinite programming, and a locally convergent SSLE method is proposed for SIP. We only need solve a linear system equations and a subproblem with a parameter per step, also a modified algorithm which saves cost of computations is given, at the end of the paper, we give a proof of the convergence for the algorithms.