A Novel Algorithm for Linear Programming

Abstract

The problem of optimizing a linear objective function, given a number of linear constraints has been a long standing problem ever since the times of Kantorovich, Dantzig and John von Neumann. These developments have been followed by a different approach pioneered by Khachiyan and Karmarkar. In this paper we attempt a new approach for solving an old optimization problem in a novel manner, in the sense that we devise a method that reduces the dimension of the problem step by step and interestingly is recursive. The method can be extended to other types of optimization problems in convex space, e.g. for solving a linear optimization problem subject to nonlinear constraints in a convex region.