Research On Newton-Type And Primal-Dual Interior Algorithms For Semidefinite Programming

The thesis is mainly about semidefinite programming problem which is one of the most attractive problems in mathematical programming area in recent years, and its algorithm is concentrated on.In chapter 1, we briefly review the development as well as research situation of semidefinite programming and then introduce the topic in the following chapters.In chapter 2, we propose a new Newton-type algorithm which has a quadratic convergence rate. The new algorithm sufficiently used the properties of smooth Fischer - Burmeister function and improved the algorithm proposed by Chen and Tseng, etc.In chapter 3, a new primal-dual interior method is proposed which overcome the shortcomings of Peng' s algorithm based on the self-regular function. The choice of parameters of the new algorithm is related to the duality gap whose changes can be predicted and reduce at each step. What' s more, each iterate of the algorithm lies in the neighborhood of the central path. Consequently, no centralized step is needed in the inner iteration.