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On Linear Inequality Systems with Smooth Coefficients

Author

Listed:
  • M. A. Goberna

    (Universidad de Alicante)

  • L. Hernández

    (Universidad Autónoma de Puebla)

  • M. I. Todorov

    (Universidad de las Américas)

Abstract

A linear inequality system with infinitely many constraints is polynomial [analytical] if its index set is a compact interval of the real line and all its coefficients are polynomial [analytical] functions of the index on this interval. This paper provides sufficient conditions for a given closed convex set to be the solution set of a certain polynomial or at least analytical system.

Suggested Citation

  • M. A. Goberna & L. Hernández & M. I. Todorov, 2005. "On Linear Inequality Systems with Smooth Coefficients," Journal of Optimization Theory and Applications, Springer, vol. 124(2), pages 363-386, February.
    • Handle: RePEc:spr:joptap:v:124:y:2005:i:2:d:10.1007_s10957-004-0941-1
    DOI: 10.1007/s10957-004-0941-1
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    References listed on IDEAS

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    1. M. A. Goberna & V. Jornet & R. Puente & M. I. Todorov, 1999. "Analytical Linear Inequality Systems and Optimization," Journal of Optimization Theory and Applications, Springer, vol. 103(1), pages 95-119, October.
    2. Leon, Teresa & Vercher, Enriqueta, 1992. "A purification algorithm for semi-infinite programming," European Journal of Operational Research, Elsevier, vol. 57(3), pages 412-420, March.
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    Citations

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    Cited by:

    1. Miguel Goberna & Lidia Hernández & Maxim Todorov, 2005. "Separating the solution sets of analytical and polynomial systems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 13(2), pages 321-329, December.

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    1. M. A. Goberna & V. Jornet & R. Puente & M. I. Todorov, 1999. "Analytical Linear Inequality Systems and Optimization," Journal of Optimization Theory and Applications, Springer, vol. 103(1), pages 95-119, October.
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    3. Leon, T. & Sanmatias, S. & Vercher, E., 2000. "On the numerical treatment of linearly constrained semi-infinite optimization problems," European Journal of Operational Research, Elsevier, vol. 121(1), pages 78-91, February.

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