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A comparative note on the relaxation algorithms for the linear semi-infinite feasibility problem

Author

Listed:
  • A. Ferrer

    (Universitat Politècnica de Catalunya)

  • M. A. Goberna

    (Alicante University)

  • E. González-Gutiérrez

    (Polytechnic University of Tulancingo)

  • M. I. Todorov

    (UDLAP)

Abstract

The problem (LFP) of finding a feasible solution to a given linear semi-infinite system arises in different contexts. This paper provides an empirical comparative study of relaxation algorithms for (LFP). In this study we consider, together with the classical algorithm, implemented with different values of the fixed parameter (the step size), a new relaxation algorithm with random parameter which outperforms the classical one in most test problems whatever fixed parameter is taken. This new algorithm converges geometrically to a feasible solution under mild conditions. The relaxation algorithms under comparison have been implemented using the extended cutting angle method for solving the global optimization subproblems.

Suggested Citation

  • A. Ferrer & M. A. Goberna & E. González-Gutiérrez & M. I. Todorov, 2017. "A comparative note on the relaxation algorithms for the linear semi-infinite feasibility problem," Annals of Operations Research, Springer, vol. 258(2), pages 587-612, November.
    • Handle: RePEc:spr:annopr:v:258:y:2017:i:2:d:10.1007_s10479-016-2135-2
    DOI: 10.1007/s10479-016-2135-2
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    References listed on IDEAS

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    1. Gleb Beliakov & Albert Ferrer, 2010. "Bounded lower subdifferentiability optimization techniques: applications," Journal of Global Optimization, Springer, vol. 47(2), pages 211-231, June.
    2. E. González-Gutiérrez & L. Hernández Rebollar & Maxim Todorov, 2012. "Relaxation methods for solving linear inequality systems: converging results," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(2), pages 426-436, July.
    3. Goberna, M.A. & Jeyakumar, V. & Li, G. & Vicente-Pérez, J., 2015. "Robust solutions to multi-objective linear programs with uncertain data," European Journal of Operational Research, Elsevier, vol. 242(3), pages 730-743.
    4. A.M. Bagirov & A.M. Rubinov, 2000. "Global Minimization of Increasing Positively Homogeneous Functions over the Unit Simplex," Annals of Operations Research, Springer, vol. 98(1), pages 171-187, December.
    5. A. Auslender & A. Ferrer & M. Goberna & M. López, 2015. "Comparative study of RPSALG algorithm for convex semi-infinite programming," Computational Optimization and Applications, Springer, vol. 60(1), pages 59-87, January.
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    Cited by:

    1. Le Thanh Tung, 2022. "Karush–Kuhn–Tucker optimality conditions and duality for multiobjective semi-infinite programming with vanishing constraints," Annals of Operations Research, Springer, vol. 311(2), pages 1307-1334, April.

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