The theory of linear programming: Skew symmetric self-dual problems and the central path

作     者：Jansen, B. Roos, C. Terlaky, T. 

作者机构：Delft University of Technology Faculty of Technical Mathematics and Informatics 2600 GA Delft P.O. Box 5031 Netherlands 

出 版 物：《Optimization》 (Optimization)

年 卷 期：1994年第29卷第3期

页      面：225-233页

学科分类：0820[工学-石油与天然气工程] 12[管理学] 1201[管理学-管理科学与工程(可授管理学、工学学位)] 07[理学] 070105[理学-运筹学与控制论] 0701[理学-数学] 0811[工学-控制科学与工程] 

主　　题：complementarity duality Farkas Lemma interior points Linear programming self-dual problems skew symmetric matrix 

摘      要：The literature in the field of interior point methods for linear programming has been almostexclusively algorithm oriented. Recently Giiler, Roos, Terlaky and Vial presented a complete duality theory for linear programming based on the interior point approach. In this paper we present a more simple approach which is based on an embedding of the primal problem and its dual into a skew symmetric self-dual problem. This embedding is essentially due Ye, Todd and *** we consider a skew symmetric self-dual linear program. We show that the strong duality theorem trivially holds in this case. Then, using the logarithmic barrier problem and the central path, the existence of a strictly complementary optimal solution is proved. Using the embedding just described, we easily obtain the strong duality theorem and the existence of strictly complementary optimal solutions for general linear programming problems. © 1994, Taylor & Francis Group, LLC. All rights reserved.