Programmation Lin\'eaire, une nouvelle approche / Novel way in linear Programming

TL;DR

This paper introduces a novel linear programming approach using a simple idea of dichotomic hyperplane translations to efficiently find approximate solutions with desired accuracy.

Contribution

It presents a new algorithm for linear programming based on hyperplane translations, offering an alternative to traditional methods.

Findings

Algorithm achieves accurate approximate solutions

Method simplifies the process of solving linear programming problems

Potential for improved computational efficiency

Abstract

R\'esum\'e Apr\`es un bref aper\c{c}u permettant de situer notre travail, nous proposons une nouvelle voie pour aborder la programmation lin\'eaire en proposant un algorithme \'elabor\'e \`a partir d'une id\'ee simple qui permet d'obtenir une solution aussi approch\'ee que voulu par translation dichotomique d'un hyperplan de l'espace des solutions. Abstract After a short course in order to situate our work, we propose a new way to study linear programming and we give a proposal of algorithm to solve linear programming from a basic idea which allow to obtain an approached solution with desired accuracy. For this we use some dichotomic translations of an hyperplan in the solutions hyperspace.