Proximal methods in view of interior-point strategies

作     者：Kaplan, A Tichatschke, R 

作者机构：Tech Univ Darmstadt Dept Math D-64287 Darmstadt Germany Univ Trier Dept Math 4 Trier Germany 

出 版 物：《JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS》 (优选法理论与应用杂志)

年 卷 期：1998年第98卷第2期

页      面：399-429页

核心收录：

学科分类：1201[管理学-管理科学与工程(可授管理学、工学学位)] 07[理学] 070104[理学-应用数学] 0701[理学-数学] 

主　　题：interior-point methods convex optimization ill-posed problems proximal point algorithms 

摘      要：This paper deals with regularized penalty-barrier methods for convex programming problems. In the spirit of an iterative proximal regularization approach, an interior-point method is constructed, in which at each step a strongly convex function has to be minimized and the prox-term can be scaled by a variable scaling factor. The convergence of the method is studied for an axiomatically given class of barrier functions. According to the results, a wide class of barrier functions (in particular, logarithmic and exponential functions) can be applied to design special algorithms. For the method with a logarithmic barrier, the rate of convergence is investigated and assumptions that ensure linear convergence are given.