IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v193y2022i1d10.1007_s10957-021-01959-z.html
   My bibliography  Save this article

Two Optimal Value Functions in Parametric Conic Linear Programming

Author

Listed:
  • Nguyen Ngoc Luan

    (Hanoi National University of Education)

  • Do Sang Kim

    (Pukyong National University)

  • Nguyen Dong Yen

    (Vietnam Academy of Science and Technology)

Abstract

We consider the conic linear program given by a closed convex cone in an Euclidean space and a matrix, where vector on the right-hand side of the inequality constraint and the vector defining the objective function are subject to change. Using the strict feasibility condition, we prove the locally Lipschitz continuity and obtain some differentiability properties of the optimal value function of the problem under right-hand-side perturbations. For the optimal value function under linear perturbations of the objective function, similar differentiability properties are obtained under the assumption saying that both primal problem and dual problem are strictly feasible.

Suggested Citation

  • Nguyen Ngoc Luan & Do Sang Kim & Nguyen Dong Yen, 2022. "Two Optimal Value Functions in Parametric Conic Linear Programming," Journal of Optimization Theory and Applications, Springer, vol. 193(1), pages 574-597, June.
    • Handle: RePEc:spr:joptap:v:193:y:2022:i:1:d:10.1007_s10957-021-01959-z
    DOI: 10.1007/s10957-021-01959-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-021-01959-z
    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/s10957-021-01959-z?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. Bernhard Gollan, 1984. "On The Marginal Function in Nonlinear Programming," Mathematics of Operations Research, INFORMS, vol. 9(2), pages 208-221, May.
    2. N. D. Yen, 1997. "Stability of the Solution Set of Perturbed Nonsmooth Inequality Systems and Application," Journal of Optimization Theory and Applications, Springer, vol. 93(1), pages 199-225, April.
    3. Yoshiyuki Sekiguchi & Hayato Waki, 2021. "Perturbation Analysis of Singular Semidefinite Programs and Its Applications to Control Problems," Journal of Optimization Theory and Applications, Springer, vol. 188(1), pages 52-72, January.
    4. E. A. Yildirim, 2004. "Unifying Optimal Partition Approach to Sensitivity Analysis in Conic Optimization," Journal of Optimization Theory and Applications, Springer, vol. 122(2), pages 405-423, August.
    5. David G. Luenberger & Yinyu Ye, 2016. "Linear and Nonlinear Programming," International Series in Operations Research and Management Science, Springer, edition 4, number 978-3-319-18842-3, December.
    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. Nguyen Ngoc Luan & Nguyen Dong Yen, 2024. "Strong Duality and Solution Existence Under Minimal Assumptions in Conic Linear Programming," Journal of Optimization Theory and Applications, Springer, vol. 203(2), pages 1083-1102, November.

    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. François Le Grand & Xavier Ragot, 2022. "Managing Inequality Over Business Cycles: Optimal Policies With Heterogeneous Agents And Aggregate Shocks," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 63(1), pages 511-540, February.
    2. Gui-Hua Lin & Mei-Ju Luo & Jin Zhang, 2016. "Smoothing and SAA method for stochastic programming problems with non-smooth objective and constraints," Journal of Global Optimization, Springer, vol. 66(3), pages 487-510, November.
    3. Sandra S. Y. Tan & Antonios Varvitsiotis & Vincent Y. F. Tan, 2021. "Analysis of Optimization Algorithms via Sum-of-Squares," Journal of Optimization Theory and Applications, Springer, vol. 190(1), pages 56-81, July.
    4. Michael K. McWilliam & Antariksh C. Dicholkar & Frederik Zahle & Taeseong Kim, 2022. "Post-Optimum Sensitivity Analysis with Automatically Tuned Numerical Gradients Applied to Swept Wind Turbine Blades," Energies, MDPI, vol. 15(9), pages 1-19, April.
    5. Wenqiang Dai & Meng Zheng & Xu Chen & Zhuolin Yang, 0. "Online economic ordering problem for deteriorating items with limited price information," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-23.
    6. Kohei Hasui & Teruyoshi Kobayashi & Tomohiro Sugo, 2019. "Irreversible monetary policy at the zero lower bound," Discussion Papers 1906, Graduate School of Economics, Kobe University.
    7. A. Uderzo, 2014. "On Lipschitz Semicontinuity Properties of Variational Systems with Application to Parametric Optimization," Journal of Optimization Theory and Applications, Springer, vol. 162(1), pages 47-78, July.
    8. Hedlund, Jonas, 2017. "Bayesian persuasion by a privately informed sender," Journal of Economic Theory, Elsevier, vol. 167(C), pages 229-268.
    9. 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.
    10. Vu Thi Huong & Jen-Chih Yao & Nguyen Dong Yen, 2017. "On the Stability and Solution Sensitivity of a Consumer Problem," Journal of Optimization Theory and Applications, Springer, vol. 175(2), pages 567-589, November.
    11. Janosch Rieger, 2021. "A Galerkin approach to optimization in the space of convex and compact subsets of $${\mathbb {R}}^d$$ R d," Journal of Global Optimization, Springer, vol. 79(3), pages 593-615, March.
    12. N. Huy & D. Kim, 2013. "Lipschitz behavior of solutions to nonconvex semi-infinite vector optimization problems," Journal of Global Optimization, Springer, vol. 56(2), pages 431-448, June.
    13. Hasui, Kohei & Kobayashi, Teruyoshi & Sugo, Tomohiro, 2021. "Optimal irreversible monetary policy," European Economic Review, Elsevier, vol. 134(C).
    14. Wenqiang Dai & Meng Zheng & Xu Chen & Zhuolin Yang, 2022. "Online economic ordering problem for deteriorating items with limited price information," Journal of Combinatorial Optimization, Springer, vol. 44(4), pages 2246-2268, November.
    15. Duong Thi Viet An & Jen-Chih Yao, 2016. "Further Results on Differential Stability of Convex Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 170(1), pages 28-42, July.
    16. Er-Rahmadi, Btissam & Ma, Tiejun, 2022. "Data-driven mixed-Integer linear programming-based optimisation for efficient failure detection in large-scale distributed systems," European Journal of Operational Research, Elsevier, vol. 303(1), pages 337-353.
    17. Neculai Andrei, 2020. "Diagonal Approximation of the Hessian by Finite Differences for Unconstrained Optimization," Journal of Optimization Theory and Applications, Springer, vol. 185(3), pages 859-879, June.
    18. Ibrahem, Ibrahem M.A. & Akhrif, Ouassima & Moustapha, Hany & Staniszewski, Martin, 2021. "Nonlinear generalized predictive controller based on ensemble of NARX models for industrial gas turbine engine," Energy, Elsevier, vol. 230(C).
    19. Michael N. Vrahatis & Panagiotis Kontogiorgos & George P. Papavassilopoulos, 2020. "Particle Swarm Optimization for Computing Nash and Stackelberg Equilibria in Energy Markets," SN Operations Research Forum, Springer, vol. 1(3), pages 1-23, September.
    20. Jason Xu & Eric C. Chi & Meng Yang & Kenneth Lange, 2018. "A majorization–minimization algorithm for split feasibility problems," Computational Optimization and Applications, Springer, vol. 71(3), pages 795-828, December.

    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:193:y:2022:i:1:d:10.1007_s10957-021-01959-z. 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.