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Extremality, Stationarity and Generalized Separation of Collections of Sets

Author

Listed:
  • Hoa T. Bui

    (Federation University Australia)

  • Alexander Y. Kruger

    (Federation University Australia)

Abstract

The core arguments used in various proofs of the extremal principle and its extensions as well as in primal and dual characterizations of approximate stationarity and transversality of collections of sets are exposed, analysed and refined, leading to a unifying theory, encompassing all existing approaches to obtaining ‘extremal’ statements. For that, we examine and clarify quantitative relationships between the parameters involved in the respective definitions and statements. Some new characterizations of extremality properties are obtained.

Suggested Citation

  • Hoa T. Bui & Alexander Y. Kruger, 2019. "Extremality, Stationarity and Generalized Separation of Collections of Sets," Journal of Optimization Theory and Applications, Springer, vol. 182(1), pages 211-264, July.
    • Handle: RePEc:spr:joptap:v:182:y:2019:i:1:d:10.1007_s10957-018-01458-8
    DOI: 10.1007/s10957-018-01458-8
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    References listed on IDEAS

    as
    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.
    2. Jonathan M. Borwein & Alejandro Jofré, 1998. "A nonconvex separation property in Banach spaces," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 48(2), pages 169-179, November.
    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.
    Full references (including those not matched with items on IDEAS)

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