A New Algorithm for Linear Programming

Details A New Algorithm for Linear Programming A New Algorithm for Linear Programming

2006-04-07

arxiv.org/abs/math/0604171v1

Mathematics

General Mathematics

Scientific paper

In this paper we discuss a new algorithm for linear programming. It is based on treating the objective function (the linear form) as a parameter and developing the system of equations in the reduced row echelon form. The fixing of the values of certain variables to zero is carried out by exploiting their logical relation with the optimization process. The optimal value is then obtained by solving certain subsystem of equations. A binary search type alternative algorithm for linear programs is then proposed. We then show that the idea of condensing the objective function as a parameter naturally extends to deal with nonlinear and integer programs by making use of the technique of respectively Grobner bases and the methods of solving linear Diophantine equations. Various examples are discussed from time to time to elaborate the ideas proposed in this paper.

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