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Uniform LP duality for semidefinite and semi-infinite programming

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  • Qinghong Zhang

Abstract

Recently, a semidefinite and semi-infinite linear programming problem (SDSIP), its dual (DSDSIP), and uniform LP duality between (SDSIP) and (DSDSIP) were proposed and studied by Li et al. (Optimization 52:507–528, 2003). In this paper, we show that (SDSIP) is an ordinary linear semi-infinite program and, therefore, all the existing results regarding duality and uniform LP duality for linear semi-infinite programs can be applied to (SDSIP). By this approach, the main results of Li et al. (Optimization 52:507–528, 2003) can be obtained easily. Copyright Springer-Verlag 2008

Suggested Citation

  • Qinghong Zhang, 2008. "Uniform LP duality for semidefinite and semi-infinite programming," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 16(2), pages 205-213, June.
    • Handle: RePEc:spr:cejnor:v:16:y:2008:i:2:p:205-213
    DOI: 10.1007/s10100-007-0048-5
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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. R. J. Duffin & L. A. Karlovitz, 1965. "An Infinite Linear Program with a Duality Gap," Management Science, INFORMS, vol. 12(1), pages 122-134, September.
    3. 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.
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    Cited by:

    1. Martin Gavalec & Karel Zimmermann, 2012. "Duality for max-separable problems," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 20(3), pages 409-419, September.
    2. O. I. Kostyukova & T. V. Tchemisova & O. S. Dudina, 2024. "On the Uniform Duality in Copositive Optimization," Journal of Optimization Theory and Applications, Springer, vol. 203(2), pages 1940-1966, November.

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