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Quantitative Characterizations of Regularity Properties of Collections of Sets

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  • Alexander Y. Kruger

    (Federation University Australia)

  • Nguyen H. Thao

    (Federation University Australia)

Abstract

Several primal and dual quantitative characterizations of regularity properties of collections of sets in normed linear spaces are discussed. Relationships between regularity properties of collections of sets and those of set-valued mappings are provided.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:164:y:2015:i:1:d:10.1007_s10957-014-0556-0
    DOI: 10.1007/s10957-014-0556-0
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    References listed on IDEAS

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    1. Hédy Attouch & Jérôme Bolte & Patrick Redont & Antoine Soubeyran, 2010. "Proximal Alternating Minimization and Projection Methods for Nonconvex Problems: An Approach Based on the Kurdyka-Łojasiewicz Inequality," Mathematics of Operations Research, INFORMS, vol. 35(2), pages 438-457, May.
    2. 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.
    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. Francisco Aragón Artacho & Boris Mordukhovich, 2011. "Enhanced metric regularity and Lipschitzian properties of variational systems," Journal of Global Optimization, Springer, vol. 50(1), pages 145-167, May.
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    Cited by:

    1. Marius Durea & Diana Maxim & Radu Strugariu, 2021. "Metric Inequality Conditions on Sets and Consequences in Optimization," Journal of Optimization Theory and Applications, Springer, vol. 189(3), pages 744-771, June.
    2. 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.
    3. Nguyen Hieu Thao, 2018. "A convergent relaxation of the Douglas–Rachford algorithm," Computational Optimization and Applications, Springer, vol. 70(3), pages 841-863, July.
    4. D. Russell Luke & Nguyen H. Thao & Matthew K. Tam, 2018. "Quantitative Convergence Analysis of Iterated Expansive, Set-Valued Mappings," Mathematics of Operations Research, INFORMS, vol. 43(4), pages 1143-1176, November.

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