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An infeasible interior-point arc-search method with Nesterov’s restarting strategy for linear programming problems

Author

Listed:
  • Einosuke Iida

    (Tokyo Institute of Technology)

  • Makoto Yamashita

    (Tokyo Institute of Technology)

Abstract

An arc-search interior-point method is a type of interior-point method that approximates the central path by an ellipsoidal arc, and it can often reduce the number of iterations. In this work, to further reduce the number of iterations and the computation time for solving linear programming problems, we propose two arc-search interior-point methods using Nesterov’s restarting strategy which is a well-known method to accelerate the gradient method with a momentum term. The first one generates a sequence of iterations in the neighborhood, and we prove that the proposed method converges to an optimal solution and that it is a polynomial-time method. The second one incorporates the concept of the Mehrotra-type interior-point method to improve numerical performance. The numerical experiments demonstrate that the second one reduced the number of iterations and the computational time compared to existing interior-point methods due to the momentum term.

Suggested Citation

  • Einosuke Iida & Makoto Yamashita, 2024. "An infeasible interior-point arc-search method with Nesterov’s restarting strategy for linear programming problems," Computational Optimization and Applications, Springer, vol. 88(2), pages 643-676, June.
    • Handle: RePEc:spr:coopap:v:88:y:2024:i:2:d:10.1007_s10589-024-00561-z
    DOI: 10.1007/s10589-024-00561-z
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    References listed on IDEAS

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    1. Yang, Yaguang, 2011. "A polynomial arc-search interior-point algorithm for convex quadratic programming," European Journal of Operational Research, Elsevier, vol. 215(1), pages 25-38, November.
    2. Luiz-Rafael Santos & Fernando Villas-Bôas & Aurelio R. L. Oliveira & Clovis Perin, 2019. "Optimized choice of parameters in interior-point methods for linear programming," Computational Optimization and Applications, Springer, vol. 73(2), pages 535-574, June.
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