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Validated Infeasible Interior-Point Predictor–Corrector Methods for Linear Programming

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Abstract

Many problems arising in practical applications lead to linear programming problems. Hence, they are fundamentally tractable. Recent interior-point methods can exploit problem structure to solve such problems very efficiently. Infeasible interior-point predictor–corrector methods using floating-point arithmetic sometimes compute an approximate solution with duality gap less than a given tolerance even when the problem may not have a solution. We present an efficient verification method for solving linear programming problems which computes a guaranteed enclosure of the optimal solution and which verifies the existence of the solution within the computed interval.

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Authors and Affiliations

  1. Institute for Applied Research, University of Applied Sciences, FH Konstanz, D-78405, Konstanz, Germany

    Ismail I. Idriss

  2. Institute of Scientific Computing, Dresden University of Technology, D-01062, Dresden, Germany

    Wolfgang V. Walter

Authors
  1. Ismail I. Idriss
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  2. Wolfgang V. Walter
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Idriss, I.I., Walter, W.V. Validated Infeasible Interior-Point Predictor–Corrector Methods for Linear Programming. Numerical Algorithms 37, 177–185 (2004). https://doi.org/10.1023/B:NUMA.0000049465.66643.ce

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