Linear Programming Using ABS Method

Abstract

Nowadays, we face many equations in everyday life, where many attempts have been made to find their solutions, and various methods have been introduced. Many complex problems often lead to the solution of systems of equations. In mathematics, linear programming problems is a technique for optimization of a linear objective function that must impose several constraints on linear inequality. Linear programming emerged as a mathematical model. In this study, we introduce the category of ABS methods to solve general linear equations. These methods have been developed by Abafi, Goin, and Speedicato, and the repetitive methods are of direct type, which implicitly includes LU decomposition, Cholesky decomposition, LX decomposition, etc. Methods are distinguished from each other by selecting parameters. First, the equations system and the methods of solving the equations system, along with their application, are examined. Introduction and history of linear programming and linear programming problems and their application were also discussed.