SOME PROPERTIES OF GENERALIZED PROXIMAL POINT METHODS FOR QUADRATIC AND LINEAR-PROGRAMMING

作     者：IUSEM, AN 

作者机构：Instituto de Matemática Pura e Aplicada Rio de Janeiro Brazil 

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

年 卷 期：1995年第85卷第3期

页      面：593-612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：PROXIMAL POINT METHODS CONVEX PROGRAMMING QUADRATIC PROGRAMMING LINEAR PROGRAMMING 

摘      要：The proximal point method for convex optimization has been extended recently through the use of generalized distances (e.g., Bregman distances) instead of the Euclidean one. One advantage of these extensions is the possibility of eliminating certain constraints (mainly positivity) from the subproblems, transforming an inequality constrained problem into a sequence of unconstrained or equality constrained problems. We consider here methods obtained using a certain class of Bregman functions applied to convex quadratic (including linear) programming, which are of the interior-point type. We prove that the limit of the sequence generated by the method lies in the relative interior of the solution set, and furthermore is the closest optimal solution to the initial point, in the sense of the Bregman distance. These results do not hold for the standard proximal point method, i.e., when the square of the Euclidean norm is used as the Bregman distance.