The row pivoting method for linear programming

作     者：Liu, Yanwu Tu, Yan Zhang, Zhongzhen 

作者机构：Wuhan Univ Technol Sch Safety Sci & Emergency Management Wuhan 430070 Peoples R China Wuhan Univ Technol Sch Management Wuhan 430070 Peoples R China 

出 版 物：《OMEGA-INTERNATIONAL JOURNAL OF MANAGEMENT SCIENCE》 (国际管理科学杂志)

年 卷 期：2021年第100卷

页      面：102354-102354页

核心收录：

学科分类：12[管理学] 120202[管理学-企业管理（含：财务管理、市场营销、人力资源管理）] 0202[经济学-应用经济学] 02[经济学] 1202[管理学-工商管理] 1201[管理学-管理科学与工程(可授管理学、工学学位)] 

基　　金：National Natural Science Foundation of China Humanities and Social Science Fund of Ministry of Education of China [18YJC630163] Fundamental Research Funds for the Central Universities WUT [2020VI006, WUT: 2020VI008] 

主　　题：The row pivoting method Linear programming Farkas lemma 

摘      要：Solving linear programming is essentially to solve a special system of linear inequalities. Unlike other pivoting methods, we find that row geometry can fully and effectively exploit huge potential of Farkas Lemma in solving systems of linear inequalities and is a feasible way to solve linear programming. Therefore, we develop the row pivoting method for solving linear programming. The central idea of this method is to solve a system of linear inequalities corresponding to constraints of linear programming while keeping the optimality condition true all the time. In the proposed method, any linear programming problem can be solved without imposing redundancy or consistency assumptions, equations and inequalities in the constraints can be directly expressed in row vector form free of any auxiliary variables. The method can identify inconsistency and redundancy of constraints inherently, start with an arbitrary basic solution directly, eliminate equation constraints efficiently, and treat lower and upper bounds on any inequality constraint simultaneously. The proof of existence and convergence guarantees that the method can determine whether there exists an optimal solution to linear programming in finitely many steps. (C) 2020 Elsevier Ltd. All rights reserved.