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Analytical Linear Inequality Systems and Optimization

Author

Listed:
  • M. A. Goberna

    (University of Alicante)

  • V. Jornet

    (University of Alicante)

  • R. Puente

    (National University of San Luis)

  • M. I. Todorov

    (Bulgarian Academy of Sciences)

Abstract

In many interesting semi-infinite programming problems, all the constraints are linear inequalities whose coefficients are analytical functions of a one-dimensional parameter. This paper shows that significant geometrical information on the feasible set of these problems can be obtained directly from the given coefficient functions. One of these geometrical properties gives rise to a general purification scheme for linear semi-infinite programs equipped with so-called analytical constraint systems. It is also shown that the solution sets of such kind of consistent systems form a transition class between polyhedral convex sets and closed convex sets in the Euclidean space of the unknowns.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:103:y:1999:i:1:d:10.1023_a:1021773300365
    DOI: 10.1023/A:1021773300365
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    References listed on IDEAS

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    1. A. Charnes & W. W. Cooper & K. Kortanek, 1965. "On Representations of Semi-Infinite Programs which Have No Duality Gaps," Management Science, INFORMS, vol. 12(1), pages 113-121, September.
    2. A. Charnes & W. W. Cooper & K. Kortanek, 1963. "Duality in Semi-Infinite Programs and Some Works of Haar and Carathéodory," Management Science, INFORMS, vol. 9(2), pages 209-228, January.
    3. 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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    Cited by:

    1. 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.
    2. Goberna, M. A. & Lopez, M. A., 2002. "Linear semi-infinite programming theory: An updated survey," European Journal of Operational Research, Elsevier, vol. 143(2), pages 390-405, December.

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