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Stationarity and Regularity of Infinite Collections of Sets. Applications to Infinitely Constrained Optimization

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  • Alexander Y. Kruger

    (University of Ballarat)

  • Marco A. López

    (University of Alicante)

Abstract

This article continues the investigation of stationarity and regularity properties of infinite collections of sets in a Banach space started in Kruger and López (J. Optim. Theory Appl. 154(2), 2012), and is mainly focused on the application of the stationarity criteria to infinitely constrained optimization problems. We consider several settings of optimization problems which involve (explicitly or implicitly) infinite collections of sets and deduce for them necessary conditions characterizing stationarity in terms of dual space elements—normals and/or subdifferentials.

Suggested Citation

  • Alexander Y. Kruger & Marco A. López, 2012. "Stationarity and Regularity of Infinite Collections of Sets. Applications to Infinitely Constrained Optimization," Journal of Optimization Theory and Applications, Springer, vol. 155(2), pages 390-416, November.
    • Handle: RePEc:spr:joptap:v:155:y:2012:i:2:d:10.1007_s10957-012-0086-6
    DOI: 10.1007/s10957-012-0086-6
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    References listed on IDEAS

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    1. O. I. Kostyukova & T. V. Tchemisova & S. A. Yermalinskaya, 2010. "Convex Semi-Infinite Programming: Implicit Optimality Criterion Based on the Concept of Immobile Indices," Journal of Optimization Theory and Applications, Springer, vol. 145(2), pages 325-342, May.
    2. M. A. Goberna & T. Terlaky & M. I. Todorov, 2010. "Sensitivity Analysis in Linear Semi-Infinite Programming via Partitions," Mathematics of Operations Research, INFORMS, vol. 35(1), pages 14-26, February.
    3. Alexander Y. Kruger & Marco A. López, 2012. "Stationarity and Regularity of Infinite Collections of Sets," Journal of Optimization Theory and Applications, Springer, vol. 154(2), pages 339-369, August.
    4. Nader Kanzi, 2011. "Necessary optimality conditions for nonsmooth semi-infinite programming problems," Journal of Global Optimization, Springer, vol. 49(4), pages 713-725, April.
    5. Alfred Auslender & Miguel A. Goberna & Marco A. López, 2009. "Penalty and Smoothing Methods for Convex Semi-Infinite Programming," Mathematics of Operations Research, INFORMS, vol. 34(2), pages 303-319, May.
    6. M. J. Cánovas & A. Hantoute & M. A. López & J. Parra, 2008. "Stability of Indices in the KKT Conditions and Metric Regularity in Convex Semi-Infinite Optimization," Journal of Optimization Theory and Applications, Springer, vol. 139(3), pages 485-500, December.
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    Cited by:

    1. Alexander Y. Kruger & Nguyen H. Thao, 2015. "Quantitative Characterizations of Regularity Properties of Collections of Sets," Journal of Optimization Theory and Applications, Springer, vol. 164(1), pages 41-67, January.

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