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Implementation of warm-start strategies in interior-point methods for linear programming in fixed dimension

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Abstract

We implement several warm-start strategies in interior-point methods for linear programming (LP). We study the situation in which both the original LP instance and the perturbed one have exactly the same dimensions. We consider different types of perturbations of data components of the original instance and different sizes of each type of perturbation. We modify the state-of-the-art interior-point solver PCx in our implementation. We evaluate the effectiveness of each warm-start strategy based on the number of iterations and the computation time in comparison with “cold start” on the NETLIB test suite. Our experiments reveal that each of the warm-start strategies leads to a reduction in the number of interior-point iterations especially for smaller perturbations and for perturbations of fewer data components in comparison with cold start. On the other hand, only one of the warm-start strategies exhibits better performance than cold start in terms of computation time. Based on the insight gained from the computational results, we discuss several potential improvements to enhance the performances of such warm-start strategies.

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Authors and Affiliations

  1. Automatic Data Processing, Inc., Edgewood, NY, 11717, USA

    Elizabeth John

  2. Department of Industrial Engineering, Bilkent University, 06800 Bilkent, Ankara, Turkey

    E. Alper Yıldırım

Authors
  1. Elizabeth John
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  2. E. Alper Yıldırım
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Correspondence to E. Alper Yıldırım.

Additional information

This research was supported in part by NSF through CAREER grant DMI-0237415.

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John, E., Yıldırım, E.A. Implementation of warm-start strategies in interior-point methods for linear programming in fixed dimension. Comput Optim Appl 41, 151–183 (2008). https://doi.org/10.1007/s10589-007-9096-y

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  • DOI: https://doi.org/10.1007/s10589-007-9096-y

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