IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v171y2016i3d10.1007_s10957-015-0807-8.html
   My bibliography  Save this article

Nonlinear Metric Subregularity

Author

Listed:
  • Alexander Y. Kruger

    (Federation University Australia)

Abstract

In this article, we investigate nonlinear metric subregularity properties of set-valued mappings between general metric or Banach spaces. We demonstrate that these properties can be treated in the framework of the theory of (linear) error bounds for extended real-valued functions of two variables developed in Kruger (Error bounds and metric subregularity. Optimization 64(1):49–79, 2015). Several primal and dual space local quantitative and qualitative criteria of nonlinear metric subregularity are formulated. The relationships between the criteria are established and illustrated.

Suggested Citation

  • Alexander Y. Kruger, 2016. "Nonlinear Metric Subregularity," Journal of Optimization Theory and Applications, Springer, vol. 171(3), pages 820-855, December.
    • Handle: RePEc:spr:joptap:v:171:y:2016:i:3:d:10.1007_s10957-015-0807-8
    DOI: 10.1007/s10957-015-0807-8
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-015-0807-8
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10957-015-0807-8?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Marian J. Fabian & René Henrion & Alexander Y. Kruger & Jiří V. Outrata, 2012. "About error bounds in metric spaces," Operations Research Proceedings, in: Diethard Klatte & Hans-Jakob Lüthi & Karl Schmedders (ed.), Operations Research Proceedings 2011, edition 127, pages 33-38, Springer.
    2. Diethard Klatte & Hans-Jakob Lüthi & Karl Schmedders (ed.), 2012. "Operations Research Proceedings 2011," Operations Research Proceedings, Springer, edition 127, number 978-3-642-29210-1, May.
    3. Huynh Van Ngai & Phan Nhat Tinh, 2015. "Metric Subregularity of Multifunctions: First and Second Order Infinitesimal Characterizations," Mathematics of Operations Research, INFORMS, vol. 40(3), pages 703-724, March.
    4. Boris Mordukhovich & Wei Ouyang, 2015. "Higher-order metric subregularity and its applications," Journal of Global Optimization, Springer, vol. 63(4), pages 777-795, December.
    5. O. Cornejo & A. Jourani & C. Zălinescu, 1997. "Conditioning and Upper-Lipschitz Inverse Subdifferentials in Nonsmooth Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 95(1), pages 127-148, October.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Huynh Ngai & Nguyen Huu Tron & Michel Théra, 2016. "Directional Hölder Metric Regularity," Journal of Optimization Theory and Applications, Springer, vol. 171(3), pages 785-819, December.
    2. Amos Uderzo, 2016. "A Strong Metric Subregularity Analysis of Nonsmooth Mappings Via Steepest Displacement Rate," Journal of Optimization Theory and Applications, Springer, vol. 171(2), pages 573-599, November.
    3. Huynh Van Ngai & Nguyen Huu Tron & Michel Théra, 2014. "Metric Regularity of the Sum of Multifunctions and Applications," Journal of Optimization Theory and Applications, Springer, vol. 160(2), pages 355-390, February.
    4. Huynh Van Ngai & Michel Théra, 2015. "Directional Metric Regularity of Multifunctions," Mathematics of Operations Research, INFORMS, vol. 40(4), pages 969-991, October.
    5. Gabriel Frahm, 2018. "An Intersection–Union Test for the Sharpe Ratio," Risks, MDPI, vol. 6(2), pages 1-13, April.
    6. Jürgen Fleiß & Ulrike Leopold‐Wildburger, 2014. "Once Nice, Always Nice? Results on Factors Influencing Nice Behavior from an Iterated Prisoner's Dilemma Experiment," Systems Research and Behavioral Science, Wiley Blackwell, vol. 31(2), pages 327-334, March.
    7. C. Zălinescu, 2003. "A Nonlinear Extension of Hoffman's Error Bounds for Linear Inequalities," Mathematics of Operations Research, INFORMS, vol. 28(3), pages 524-532, August.
    8. Mayer, Stefan & Klein, Robert & Seiermann, Stephanie, 2013. "A simulation-based approach to price optimisation of the mixed bundling problem with capacity constraints," International Journal of Production Economics, Elsevier, vol. 145(2), pages 584-598.
    9. A. Jourani & D. Zagrodny, 2012. "The positiveness of lower limits of the Hoffman constant in parametric polyhedral programs," Journal of Global Optimization, Springer, vol. 53(4), pages 641-661, August.
    10. Ruslan Sadykov & François Vanderbeck & Artur Pessoa & Issam Tahiri & Eduardo Uchoa, 2019. "Primal Heuristics for Branch and Price: The Assets of Diving Methods," INFORMS Journal on Computing, INFORMS, vol. 31(2), pages 251-267, April.
    11. Radu Boţ & Ernö Csetnek, 2012. "Error bound results for convex inequality systems via conjugate duality," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(2), pages 296-309, July.
    12. Emanuel Canelas & Tânia Pinto-Varela & Bartosz Sawik, 2020. "Electricity Portfolio Optimization for Large Consumers: Iberian Electricity Market Case Study," Energies, MDPI, vol. 13(9), pages 1-21, May.
    13. Tadeusz Sawik, 2018. "Selection of a dynamic supply portfolio under delay and disruption risks," International Journal of Production Research, Taylor & Francis Journals, vol. 56(1-2), pages 760-782, January.
    14. Lehnfeld, Jana & Knust, Sigrid, 2014. "Loading, unloading and premarshalling of stacks in storage areas: Survey and classification," European Journal of Operational Research, Elsevier, vol. 239(2), pages 297-312.
    15. Andresson Silva Firmino & Ricardo Martins Abreu Silva & Valéria Cesário Times, 2019. "A reactive GRASP metaheuristic for the container retrieval problem to reduce crane’s working time," Journal of Heuristics, Springer, vol. 25(2), pages 141-173, April.
    16. Suyabatmaz, Ali Çetin & Şahin, Güvenç, 2015. "Railway crew capacity planning problem with connectivity of schedules," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 84(C), pages 88-100.
    17. Andrea Manno & Laura Palagi & Simone Sagratella, 2019. "Case Article—Production and Distribution Optimization of Beach Equipment for the Marinero Company," INFORMS Transactions on Education, INFORMS, vol. 19(3), pages 152-154, May.
    18. Zhang, Jingran & Onal, Sevilay & Das, Sanchoy, 2020. "The dynamic stocking location problem – Dispersing inventory in fulfillment warehouses with explosive storage," International Journal of Production Economics, Elsevier, vol. 224(C).
    19. Timo Berthold, 2018. "A computational study of primal heuristics inside an MI(NL)P solver," Journal of Global Optimization, Springer, vol. 70(1), pages 189-206, January.
    20. Matthieu Maréchal, 2018. "Metric Subregularity in Generalized Equations," Journal of Optimization Theory and Applications, Springer, vol. 176(3), pages 541-558, March.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:joptap:v:171:y:2016:i:3:d:10.1007_s10957-015-0807-8. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.