Linear Optimization by Conical Projection

TL;DR

This paper introduces a novel approach to linear optimization that enhances numerical efficiency by reducing the problem to a single projection onto a convex cone, simplifying the solution process.

Contribution

It provides a theoretical foundation for solving linear optimization problems through conical projection, offering a simplified and potentially more efficient method.

Findings

Linear optimization can be solved by a single projection operation.

The approach transforms the problem into projecting onto a convex polyhedral cone.

This method simplifies the computational process for linear optimization.

Abstract

This article focuses on numerical efficiency of projection algorithms for solving linear optimization problems. The theoretical foundation for this approach is provided by the basic result that bounded finite dimensional linear optimization problem can be solved by single projection operation on the feasible polyhedron. The further simplification transforms this problem into projection of a special point onto a convex polyhedral cone generated basically by inequalities of the original linear optimization problem.