@MISC{Megiddo_onsolving, author = {Nimrod Megiddo}, title = {On Solving the Linear Programming Problem Approximately}, year = {} }

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Abstract

. This paper studies the complexity of some approximate solutions of linear programming problems with real coefficients. 1. Introduction The general linear programming problem is to maximize a linear function over a set defined by linear inequalities and equations. There are many equivalent ways to represent instances of the linear programming problem. For example, consider the symmetric form: (Sym(A; b; c)) Maximize c T x subject to Ax b x 0 : The dual is then Minimize b T y subject to A T y c y 0 : Intuitively, two representations are equivalent if there is an easy way to transform solutions of one to solutions of the other and vice versa. We first mention some of the well-known equivalences. First, any set of linear inequalities and linear equations can be reduced to a set of linear equations with nonnegativity constraints or to a set of inequality and nonnegativity constraints. Also, any linear programming problem can be reduced to a linear programming problem with a...