An analysis of the use of the Fourier-Motzkin elimination method to find an interior point to a polyhedron

• Autor(a) principal: Monticeli, André Rodrigues
• Data de Publicação: 2021
• Outros Autores: Mappa, Paulo César
• Tipo de documento: Artigo
• Idioma: por
• Título da fonte: Remat (Bento Gonçalves)
• Texto Completo: https://periodicos.ifrs.edu.br/index.php/REMAT/article/view/4305
• topic: Systems of Linear Inequalities; Polyhedron; Interior Point; Fourier-Motzkin Elimination; Sistemas de Inequações Lineares; Poliedro; Ponto Interior; Eliminação de Fourier-Motzkin

The issue of finding an interior point to a polyhedron has applications in many areas, especially in linear programming. In this work we approach the issue of finding an interior point to a polyhedron using the Fourier-Motzkin Elimination Method approach. It consists of reducing a system of linear inequalities that defines the polyhedron, by eliminating variables. A matrix version of this method was employed in order to facilitate its computational implementation, and some examples were presented with the purpose of illustrating the proposed methodology. Subsequently the complexity analysis of the algorithm was carried out in order to investigate the behavior of the technique when increasing the number of variables and restrictions and, thus, presenting a field of application to the technique. By analyzing the algorithm, we concluded that it has exponential complexity, since the number of inequalities grows exponentially as the number of variables in the issue increases. The algorithm proved to be efficient for issue with a small number of inequalities for R2 and R3.