Abstract

BUITRAGO, Oscar Y  and  RAMIREZ, Andrés L. Determination of a Starting Point in Interior Point Algorithms for solving Linear Programming Problems. Inf. tecnol. [online]. 2017, vol.28, n.5, pp.23-30. ISSN 0718-0764.  http://dx.doi.org/10.4067/S0718-07642017000500004.

This paper presents a study done to find an interior point in the feasible region of linear programming problems is an aspect that should be solved in the initial stage of the implementation of the interior point algorithms used to optimize them. Consequently, it is proposed a methodology that starts with a formulation that does not require adding surplus or slack variables. It only includes an additional variable to generate a polyhedron in a new expanded space and with simple projections finds an interior point in the same polyhedron. It is demonstrated that the optimal solution of the extended linear programming problem allows obtaining a feasible point of the original problem or concluding that it has no feasible solutions.

Keywords : linear programming; polyhedron; optimization; orthogonal projections; interior point algorithm.

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