Funciones no lineales para la determinación de un punto interior en la región factible de problemas de programación lineal

Abstract

The primary objective of this study is to propose the use of nonlinear functions to find a feasible interior point in a region defined by the constraints of linear programming problems with the advantage of not having to use slack or surplus variables. The feasible region of linear programming problems is defined by convex sets named polyhedra that have the form Ax ≤ b and that can be bounded or unbounded. Finding an interior point (even extreme or frontier point) is not a trivial issue but is a necessary condition to initialize algorithms for solving a linear programming problem. To achieve this, unrestricted nonlinear penalty functions are applied and optimized. As a result, it is demonstrated that the optimal solution point corresponds to an interior point of the original polyhedron. It is concluded that the proposed algorithmic procedure possesses features that provide advantages for solving linear programming problems.