IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v191y2021i1d10.1007_s10957-021-01924-w.html
   My bibliography  Save this article

Radius of Robust Global Error Bound for Piecewise Linear Inequality Systems

Author

Listed:
  • Thai Doan Chuong

    (Ton Duc Thang University
    Ton Duc Thang University)

Abstract

In this paper, we consider a subclass of uncertain convex inequality systems, called a class of uncertain piecewise linear systems, where the involved functions are piecewise linear. We define a concept of radius of robust global error bound for the piecewise linear inequality system under polytope uncertainty and provide formulas for calculating the radius of robust global error bound. This is achieved by employing a dual characterization for the existence of a robust global error bound of the uncertain piecewise linear system with polytope uncertainty.

Suggested Citation

  • Thai Doan Chuong, 2021. "Radius of Robust Global Error Bound for Piecewise Linear Inequality Systems," Journal of Optimization Theory and Applications, Springer, vol. 191(1), pages 68-82, October.
    • Handle: RePEc:spr:joptap:v:191:y:2021:i:1:d:10.1007_s10957-021-01924-w
    DOI: 10.1007/s10957-021-01924-w
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-021-01924-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/s10957-021-01924-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. Jiawei Chen & Jun Li & Xiaobing Li & Yibing Lv & Jen-Chih Yao, 2020. "Radius of Robust Feasibility of System of Convex Inequalities with Uncertain Data," Journal of Optimization Theory and Applications, Springer, vol. 184(2), pages 384-399, February.
    2. T. D. Chuong & V. Jeyakumar, 2017. "An Exact Formula for Radius of Robust Feasibility of Uncertain Linear Programs," Journal of Optimization Theory and Applications, Springer, vol. 173(1), pages 203-226, April.
    3. Goberna, M.A. & Jeyakumar, V. & Li, G. & Vicente-Pérez, J., 2015. "Robust solutions to multi-objective linear programs with uncertain data," European Journal of Operational Research, Elsevier, vol. 242(3), pages 730-743.
    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. Frauke Liers & Lars Schewe & Johannes Thürauf, 2022. "Radius of Robust Feasibility for Mixed-Integer Problems," INFORMS Journal on Computing, INFORMS, vol. 34(1), pages 243-261, January.
    2. Goberna, M.A. & Jeyakumar, V. & Li, G. & Vicente-Pérez, J., 2022. "The radius of robust feasibility of uncertain mathematical programs: A Survey and recent developments," European Journal of Operational Research, Elsevier, vol. 296(3), pages 749-763.
    3. M. A. Goberna & V. Jeyakumar & G. Li, 2021. "Calculating Radius of Robust Feasibility of Uncertain Linear Conic Programs via Semi-definite Programs," Journal of Optimization Theory and Applications, Springer, vol. 189(2), pages 597-622, May.
    4. Goberna, M.A. & Jeyakumar, V. & Li, G. & Vicente-Pérez, J., 2018. "Guaranteeing highly robust weakly efficient solutions for uncertain multi-objective convex programs," European Journal of Operational Research, Elsevier, vol. 270(1), pages 40-50.
    5. 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.
    6. Jiawei Chen & Jun Li & Xiaobing Li & Yibing Lv & Jen-Chih Yao, 2020. "Radius of Robust Feasibility of System of Convex Inequalities with Uncertain Data," Journal of Optimization Theory and Applications, Springer, vol. 184(2), pages 384-399, February.
    7. Daniel Woolnough & Niroshan Jeyakumar & Guoyin Li & Clement T Loy & Vaithilingam Jeyakumar, 2022. "Robust Optimization and Data Classification for Characterization of Huntington Disease Onset via Duality Methods," Journal of Optimization Theory and Applications, Springer, vol. 193(1), pages 649-675, June.
    8. Dranichak, Garrett M. & Wiecek, Margaret M., 2019. "On highly robust efficient solutions to uncertain multiobjective linear programs," European Journal of Operational Research, Elsevier, vol. 273(1), pages 20-30.
    9. Groetzner, Patrick & Werner, Ralf, 2022. "Multiobjective optimization under uncertainty: A multiobjective robust (relative) regret approach," European Journal of Operational Research, Elsevier, vol. 296(1), pages 101-115.
    10. Kuhn, K. & Raith, A. & Schmidt, M. & Schöbel, A., 2016. "Bi-objective robust optimisation," European Journal of Operational Research, Elsevier, vol. 252(2), pages 418-431.
    11. Morteza Rahimi & Majid Soleimani-damaneh, 2018. "Robustness in Deterministic Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 179(1), pages 137-162, October.
    12. Han Su & Feifei Dong & Yong Liu & Rui Zou & Huaicheng Guo, 2017. "Robustness-Optimality Tradeoff for Watershed Load Reduction Decision Making under Deep Uncertainty," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 31(11), pages 3627-3640, September.
    13. Jie Wang & Shengjie Li & Min Feng, 2022. "Unified Robust Necessary Optimality Conditions for Nonconvex Nonsmooth Uncertain Multiobjective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 195(1), pages 226-248, October.
    14. Johannes Thürauf, 2022. "Deciding the feasibility of a booking in the European gas market is coNP-hard," Annals of Operations Research, Springer, vol. 318(1), pages 591-618, November.
    15. Caprari, Elisa & Cerboni Baiardi, Lorenzo & Molho, Elena, 2019. "Primal worst and dual best in robust vector optimization," European Journal of Operational Research, Elsevier, vol. 275(3), pages 830-838.
    16. Elisa Caprari & Lorenzo Cerboni Baiardi & Elena Molho, 2022. "Scalarization and robustness in uncertain vector optimization problems: a non componentwise approach," Journal of Global Optimization, Springer, vol. 84(2), pages 295-320, October.
    17. Klamroth, Kathrin & Köbis, Elisabeth & Schöbel, Anita & Tammer, Christiane, 2017. "A unified approach to uncertain optimization," European Journal of Operational Research, Elsevier, vol. 260(2), pages 403-420.
    18. Jornada, Daniel & Leon, V. Jorge, 2016. "Biobjective robust optimization over the efficient set for Pareto set reduction," European Journal of Operational Research, Elsevier, vol. 252(2), pages 573-586.
    19. Erin K. Doolittle & Hervé L. M. Kerivin & Margaret M. Wiecek, 2018. "Robust multiobjective optimization with application to Internet routing," Annals of Operations Research, Springer, vol. 271(2), pages 487-525, December.
    20. Nguyen Minh Tung & Mai Duy, 2023. "Constraint qualifications and optimality conditions for robust nonsmooth semi-infinite multiobjective optimization problems," 4OR, Springer, vol. 21(1), pages 151-176, 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:191:y:2021:i:1:d:10.1007_s10957-021-01924-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.