IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v169y2016i3d10.1007_s10957-015-0793-x.html
   My bibliography  Save this article

Outer Limit of Subdifferentials and Calmness Moduli in Linear and Nonlinear Programming

Author

Listed:
  • M. J. Cánovas

    (Miguel Hernández University of Elche)

  • R. Henrion

    (Weierstrass Institute for Applied Analysis and Stochastics)

  • M. A. López

    (University of Alicante)

  • J. Parra

    (Miguel Hernández University of Elche)

Abstract

With a common background and motivation, the main contributions of this paper are developed in two different directions. Firstly, we are concerned with functions, which are the maximum of a finite amount of continuously differentiable functions of n real variables, paying special attention to the case of polyhedral functions. For these max-functions, we obtain some results about outer limits of subdifferentials, which are applied to derive an upper bound for the calmness modulus of nonlinear systems. When confined to the convex case, in addition, a lower bound on this modulus is also obtained. Secondly, by means of a Karush–Kuhn–Tucker index set approach, we are also able to provide a point-based formula for the calmness modulus of the argmin mapping of linear programming problems, without any uniqueness assumption on the optimal set. This formula still provides a lower bound in linear semi-infinite programming. Illustrative examples are given.

Suggested Citation

  • M. J. Cánovas & R. Henrion & M. A. López & J. Parra, 2016. "Outer Limit of Subdifferentials and Calmness Moduli in Linear and Nonlinear Programming," Journal of Optimization Theory and Applications, Springer, vol. 169(3), pages 925-952, June.
    • Handle: RePEc:spr:joptap:v:169:y:2016:i:3:d:10.1007_s10957-015-0793-x
    DOI: 10.1007/s10957-015-0793-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-015-0793-x
    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/s10957-015-0793-x?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. Diethard Klatte & Bernd Kummer, 2015. "On Calmness of the Argmin Mapping in Parametric Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 165(3), pages 708-719, June.
    2. David G. Luenberger & Yinyu Ye, 2008. "Linear and Nonlinear Programming," International Series in Operations Research and Management Science, Springer, edition 0, number 978-0-387-74503-9, September.
    3. Stephen M. Robinson, 1977. "A Characterization of Stability in Linear Programming," Operations Research, INFORMS, vol. 25(3), pages 435-447, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Zhou Wei & Christiane Tammer & Jen-Chih Yao, 2021. "Characterizations for Strong Abadie Constraint Qualification and Applications to Calmness," Journal of Optimization Theory and Applications, Springer, vol. 189(1), pages 1-18, April.
    2. M. A. Goberna & M. A. López, 2018. "Recent contributions to linear semi-infinite optimization: an update," Annals of Operations Research, Springer, vol. 271(1), pages 237-278, December.

    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. Giorgio & Cesare, 2018. "A Tutorial on Sensitivity and Stability in Nonlinear Programming and Variational Inequalities under Differentiability Assumptions," DEM Working Papers Series 159, University of Pavia, Department of Economics and Management.
    2. Marcel Klatt & Axel Munk & Yoav Zemel, 2022. "Limit laws for empirical optimal solutions in random linear programs," Annals of Operations Research, Springer, vol. 315(1), pages 251-278, August.
    3. Alp Atakan & Mehmet Ekmekci & Ludovic Renou, 2021. "Cross-verification and Persuasive Cheap Talk," Papers 2102.13562, arXiv.org, revised Apr 2021.
    4. Tanaka, Ken'ichiro & Toda, Alexis Akira, 2015. "Discretizing Distributions with Exact Moments: Error Estimate and Convergence Analysis," University of California at San Diego, Economics Working Paper Series qt7g23r5kh, Department of Economics, UC San Diego.
    5. Ashrafi, M. & Khanjani, M.J. & Fadaei-Kermani, E. & Barani, G.A., 2015. "Farm drainage channel network optimization by improved modified minimal spanning tree," Agricultural Water Management, Elsevier, vol. 161(C), pages 1-8.
    6. Sergey Badikov & Antoine Jacquier & Daphne Qing Liu & Patrick Roome, 2016. "No-arbitrage bounds for the forward smile given marginals," Papers 1603.06389, arXiv.org, revised Oct 2016.
    7. Szidarovszky, Ferenc & Luo, Yi, 2014. "Incorporating risk seeking attitude into defense strategy," Reliability Engineering and System Safety, Elsevier, vol. 123(C), pages 104-109.
    8. Rafał Wiśniowski & Krzysztof Skrzypaszek & Tomasz Małachowski, 2020. "Selection of a Suitable Rheological Model for Drilling Fluid Using Applied Numerical Methods," Energies, MDPI, vol. 13(12), pages 1-17, June.
    9. Yuichi Takano & Renata Sotirov, 2012. "A polynomial optimization approach to constant rebalanced portfolio selection," Computational Optimization and Applications, Springer, vol. 52(3), pages 645-666, July.
    10. Nadia Demarteau & Thomas Breuer & Baudouin Standaert, 2012. "Selecting a Mix of Prevention Strategies against Cervical Cancer for Maximum Efficiency with an Optimization Program," PharmacoEconomics, Springer, vol. 30(4), pages 337-353, April.
    11. Vittorio Nicolardi, 2013. "Simultaneously Balancing Supply--Use Tables At Current And Constant Prices: A New Procedure," Economic Systems Research, Taylor & Francis Journals, vol. 25(4), pages 409-434, December.
    12. Alina R. Battalova* & Nadezhda A. Opokina, 2018. "Economic-Mathematical Model of the Structure of Nutrition of Population in the Region," The Journal of Social Sciences Research, Academic Research Publishing Group, pages 275-280:1.
    13. Hee Su Roh & Yinyu Ye, 2015. "Market Making with Model Uncertainty," Papers 1509.07155, arXiv.org, revised Nov 2015.
    14. Takafumi Kanamori & Akiko Takeda, 2014. "Numerical study of learning algorithms on Stiefel manifold," Computational Management Science, Springer, vol. 11(4), pages 319-340, October.
    15. Minghui Lai & Weili Xue & Qian Hu, 2019. "An Ascending Auction for Freight Forwarder Collaboration in Capacity Sharing," Transportation Science, INFORMS, vol. 53(4), pages 1175-1195, July.
    16. Joao R. Faria & Peter Mcadam & Bruno Viscolani, 2023. "Monetary Policy, Neutrality, and the Environment," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 55(7), pages 1889-1906, October.
    17. Lee, Sunghoon & Yun, Seokwon & Kim, Jin-Kuk, 2019. "Development of novel sub-ambient membrane systems for energy-efficient post-combustion CO2 capture," Applied Energy, Elsevier, vol. 238(C), pages 1060-1073.
    18. G. Constante-Flores & A. J. Conejo & S. Constante-Flores, 2022. "Solving certain complementarity problems in power markets via convex programming," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(3), pages 465-491, October.
    19. M. G. Fiestras-Janeiro & I. Garcia-Jurado & J. Puerto, 2000. "The Concept of Proper Solution in Linear Programming," Journal of Optimization Theory and Applications, Springer, vol. 106(3), pages 511-525, September.
    20. I. Espejo & R. Páez & J. Puerto & A. M. Rodríguez-Chía, 2022. "Minimum cost b-matching problems with neighborhoods," Computational Optimization and Applications, Springer, vol. 83(2), pages 525-553, November.

    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:169:y:2016:i:3:d:10.1007_s10957-015-0793-x. 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.