On The Interior Point Algorithm For Optimization Problem With Free Variables

This thesis mainly considers the interior point method for optimization prob-lem with free variables. The paper consists of four chapters.Chapter 1 gives an introduction of the thesis, which mainly discusses the current development of the discussed issue, i.e. quadratic programming, conic linear programming and semidefinite programming problem with free variables, the main contribution of this paper is also listed in this chapter.In Chapter 2, based on the primal-dual barrier algorithm for linear pro-gramming, we propose a relaxed interior-point algorithm by regularizing the free variables and then establish the global convergence. Compared with the existing interior-point method, our method not only deals with the requirement of interior point method for free variables, but also solves the definition missing problem of the diagonal matrix under the regularization technique.In Chapter 3, we propose an inexact interior-point algorithm of conic linear programming, and prove its validity under the boundedness of iterates and the exactness of search direction.In Chapter 4, we propose a regularization interior point method for semidef-inite programming with free variables which is motivated by the reguarization technique of Meszaros, and establish its global convergence under the mild con-ditions.