IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v88y2024i1d10.1007_s10898-023-01304-w.html
   My bibliography  Save this article

Subdifferentials of optimal value functions under metric qualification conditions

Author

Listed:
  • Vu Thi Huong

    (Hangzhou Dianzi University
    Vietnam Academy of Science and Technology)

  • Duong Thi Viet An

    (Hangzhou Dianzi University
    Thai Nguyen University of Sciences)

  • Hong-Kun Xu

    (Hangzhou Dianzi University
    Henan Normal University)

Abstract

In this paper, by revisiting intersection rules for normal cones, we give formulas for estimating or computing the Fréchet/Mordukhovich/Moreau–Rockafellar subdifferentials of optimal value functions of constrained parametric optimization problems under metric qualification conditions. The results are then applied to derive chain rules for composite functions in both convex and nonconvex situations. Illustrative examples and comparisons to existing results, including those of Mordukhovich and Shao (Trans Amer Math Soc 348:1235–1280, 1996), Mordukhovich et al. (Math Program Ser B 116:369–396, 2009) and of An and Jourani (J Optim Theory Appl 192:82–96, 2022), are also addressed.

Suggested Citation

  • Vu Thi Huong & Duong Thi Viet An & Hong-Kun Xu, 2024. "Subdifferentials of optimal value functions under metric qualification conditions," Journal of Global Optimization, Springer, vol. 88(1), pages 253-283, January.
    • Handle: RePEc:spr:jglopt:v:88:y:2024:i:1:d:10.1007_s10898-023-01304-w
    DOI: 10.1007/s10898-023-01304-w
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10898-023-01304-w
    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/s10898-023-01304-w?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. Duong Thi Viet An & Abderrahim Jourani, 2022. "Subdifferentials of the Marginal Functions in Parametric Convex Optimization via Intersection Formulas," Journal of Optimization Theory and Applications, Springer, vol. 192(1), pages 82-96, January.
    2. Frank H. Clarke, 1976. "A New Approach to Lagrange Multipliers," Mathematics of Operations Research, INFORMS, vol. 1(2), pages 165-174, May.
    3. Jean-Paul Penot, 1998. "Cooperative behavior of functions, relations and sets," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 48(2), pages 229-246, November.
    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. Enrico Bellino, 2010. "Comment To ‘Commodity Content . . .’ By Fujimoto And Opocher," Metroeconomica, Wiley Blackwell, vol. 61(4), pages 749-753, November.
    2. Marius Durea & Radu Strugariu & Christiane Tammer, 2017. "On Some Methods to Derive Necessary and Sufficient Optimality Conditions in Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 175(3), pages 738-763, December.
    3. Elena-Andreea Florea, 2018. "Vector Optimization Problems with Generalized Functional Constraints in Variable Ordering Structure Setting," Journal of Optimization Theory and Applications, Springer, vol. 178(1), pages 94-118, July.
    4. Kuang Bai & Yixia Song & Jin Zhang, 2023. "Second-Order Enhanced Optimality Conditions and Constraint Qualifications," Journal of Optimization Theory and Applications, Springer, vol. 198(3), pages 1264-1284, September.
    5. Y. Y. Zhou & X. Q. Yang, 2009. "Duality and Penalization in Optimization via an Augmented Lagrangian Function with Applications," Journal of Optimization Theory and Applications, Springer, vol. 140(1), pages 171-188, January.
    6. Florian Scheuer & Alexander Wolitzky, 2016. "Capital Taxation under Political Constraints," American Economic Review, American Economic Association, vol. 106(8), pages 2304-2328, August.
    7. Abhishek Singh & Debdas Ghosh & Qamrul Hasan Ansari, 2024. "Inexact Newton Method for Solving Generalized Nash Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 201(3), pages 1333-1363, June.
    8. Casey Rothschild & Florian Scheuer, 2016. "Optimal Taxation with Rent-Seeking," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 83(3), pages 1225-1262.
    9. D. T. V. An & N. H. Hung & D. T. Ngoan & N. V. Tuyen, 2024. "Optimality conditions and sensitivity analysis in parametric nonconvex minimax programming," Journal of Global Optimization, Springer, vol. 90(1), pages 53-72, September.
    10. Yuntong Wang, 2014. "Envelope Theorem without Differentiability," Working Papers 1404, University of Windsor, Department of Economics.
    11. Zachary Bethune & Tai-Wei Hu & Guillaume Rocheteau, 2018. "Optimal Credit Cycles," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 27, pages 231-245, January.
    12. Ewald, Christian Oliver & Nolan, Charles, 2024. "On the adaptation of the Lagrange formalism to continuous time stochastic optimal control: A Lagrange-Chow redux," Journal of Economic Dynamics and Control, Elsevier, vol. 162(C).
    13. Marius Durea & Radu Strugariu & Christiane Tammer, 2015. "On set-valued optimization problems with variable ordering structure," Journal of Global Optimization, Springer, vol. 61(4), pages 745-767, April.
    14. Elodie Adida & Georgia Perakis, 2007. "A nonlinear continuous time optimal control model of dynamic pricing and inventory control with no backorders," Naval Research Logistics (NRL), John Wiley & Sons, vol. 54(7), pages 767-795, October.
    15. Teodor Chelmuş & Marius Durea & Elena-Andreea Florea, 2019. "Directional Pareto Efficiency: Concepts and Optimality Conditions," Journal of Optimization Theory and Applications, Springer, vol. 182(1), pages 336-365, July.
    16. Holger Scheel & Stefan Scholtes, 2000. "Mathematical Programs with Complementarity Constraints: Stationarity, Optimality, and Sensitivity," Mathematics of Operations Research, INFORMS, vol. 25(1), pages 1-22, February.
    17. Casey Rothschild & Florian Scheuer, 2014. "A Theory of Income Taxation under Multidimensional Skill Heterogeneity," NBER Working Papers 19822, National Bureau of Economic Research, Inc.
    18. Ronaldo C. Duarte, 2022. "Ground state solution for nonlocal scalar field equations involving an integro-differential operator," Partial Differential Equations and Applications, Springer, vol. 3(2), pages 1-14, April.
    19. D.P. Bertsekas & A.E. Ozdaglar, 2002. "Pseudonormality and a Lagrange Multiplier Theory for Constrained Optimization," Journal of Optimization Theory and Applications, Springer, vol. 114(2), pages 287-343, August.
    20. Nguyen Thi Hang & Jen-Chih Yao, 2016. "Sufficient conditions for error bounds of difference functions and applications," Journal of Global Optimization, Springer, vol. 66(3), pages 439-456, 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:jglopt:v:88:y:2024:i:1:d:10.1007_s10898-023-01304-w. 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.