A Novel Algorithm for Linear Programming

TL;DR

This paper introduces a new recursive algorithm for linear programming that reduces problem dimension step by step, offering a novel approach with potential extensions to nonlinear convex optimization problems.

Contribution

It presents a completely new recursive method for solving linear programming problems, differing from classical and existing approaches.

Findings

Proves the correctness of the recursive algorithm.

Demonstrates potential extension to nonlinear convex optimization.

Offers a dimension-reduction technique 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 von Neuman. These developments have been followed by a different approach pioneered by Khachiyan and Karmarkar. In this paper we present an entirely new method for solving an old optimization problem in a novel manner, a technique that reduces the dimension of the problem step by step and interestingly is recursive. A theorem which proves the correctness of the approach is given. 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.