A verification method for solutions of linear programming problems

  • Authors:

  • Ismail I. Idriss

  • Affiliations:

  • Institute for Applied Research, University of Applied Sciences / FH Konstanz, Konstanz, Germany

  • Venue:
  • PARA'04 Proceedings of the 7th international conference on Applied Parallel Computing: state of the Art in Scientific Computing
  • Year:
  • 2004

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Abstract

This paper is concerned with the verification of a solution of a linear programming problem obtained by an interior-point method. The presented method relies on a reformulation of the linear programming problem as an equivalent system of nonlinear equations and uses mean value interval extension of functions and a computational fixed point theorem. The designed algorithm proves or disproves the existence of a solution on a computer and, if it exists, encloses this solution in narrow bounds.