IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v176y2018i1d10.1007_s10957-017-1199-8.html
   My bibliography  Save this article

Approximate Optimality and Approximate Duality for Quasi Approximate Solutions in Robust Convex Semidefinite Programs

Author

Listed:
  • Liguo Jiao

    (Pukyong National University)

  • Jae Hyoung Lee

    (Pukyong National University)

Abstract

In this paper, we study quasi approximate solutions for a convex semidefinite programming problem in the face of data uncertainty. Using the robust optimization approach (worst-case approach), approximate optimality conditions and approximate duality theorems for quasi approximate solutions in robust convex semidefinite programming problems are explored under the robust characteristic cone constraint qualification. Moreover, some examples are given to illustrate the obtained results.

Suggested Citation

  • Liguo Jiao & Jae Hyoung Lee, 2018. "Approximate Optimality and Approximate Duality for Quasi Approximate Solutions in Robust Convex Semidefinite Programs," Journal of Optimization Theory and Applications, Springer, vol. 176(1), pages 74-93, January.
    • Handle: RePEc:spr:joptap:v:176:y:2018:i:1:d:10.1007_s10957-017-1199-8
    DOI: 10.1007/s10957-017-1199-8
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-017-1199-8
    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/s10957-017-1199-8?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. Joydeep Dutta & Kalyanmoy Deb & Rupesh Tulshyan & Ramnik Arora, 2013. "Approximate KKT points and a proximity measure for termination," Journal of Global Optimization, Springer, vol. 56(4), pages 1463-1499, August.
    2. J. Dutta, 2005. "Necessary optimality conditions and saddle points for approximate optimization in banach spaces," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 13(1), pages 127-143, June.
    3. T. Son & D. Kim, 2013. "ε-Mixed type duality for nonconvex multiobjective programs with an infinite number of constraints," Journal of Global Optimization, Springer, vol. 57(2), pages 447-465, October.
    4. V. Jeyakumar, 1997. "Asymptotic Dual Conditions Characterizing Optimality for Infinite Convex Programs," Journal of Optimization Theory and Applications, Springer, vol. 93(1), pages 153-165, April.
    5. Helmberg, C., 2002. "Semidefinite programming," European Journal of Operational Research, Elsevier, vol. 137(3), pages 461-482, March.
    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. Thai Doan Chuong, 2022. "Approximate solutions in nonsmooth and nonconvex cone constrained vector optimization," Annals of Operations Research, Springer, vol. 311(2), pages 997-1015, April.

    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. Nithirat Sisarat & Rabian Wangkeeree & Tamaki Tanaka, 2020. "Sequential characterizations of approximate solutions in convex vector optimization problems with set-valued maps," Journal of Global Optimization, Springer, vol. 77(2), pages 273-287, June.
    2. Bo Jiang & Tianyi Lin & Shiqian Ma & Shuzhong Zhang, 2019. "Structured nonconvex and nonsmooth optimization: algorithms and iteration complexity analysis," Computational Optimization and Applications, Springer, vol. 72(1), pages 115-157, January.
    3. Jeyakumar, V. & Lee, G.M. & Dinh, N., 2006. "Characterizations of solution sets of convex vector minimization problems," European Journal of Operational Research, Elsevier, vol. 174(3), pages 1380-1395, November.
    4. V. Jeyakumar & G. M. Lee & N. Dinh, 2004. "Lagrange Multiplier Conditions Characterizing the Optimal Solution Sets of Cone-Constrained Convex Programs," Journal of Optimization Theory and Applications, Springer, vol. 123(1), pages 83-103, October.
    5. Mohamed Abouhawwash & Kalyanmoy Deb, 2021. "Reference point based evolutionary multi-objective optimization algorithms with convergence properties using KKTPM and ASF metrics," Journal of Heuristics, Springer, vol. 27(4), pages 575-614, August.
    6. Thai Doan Chuong, 2022. "Approximate solutions in nonsmooth and nonconvex cone constrained vector optimization," Annals of Operations Research, Springer, vol. 311(2), pages 997-1015, April.
    7. Xiangkai Sun & Kok Lay Teo & Xian-Jun Long, 2021. "Some Characterizations of Approximate Solutions for Robust Semi-infinite Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 191(1), pages 281-310, October.
    8. C. Gutiérrez & R. López & J. Martínez, 2022. "Generalized $${\varepsilon }$$ ε -quasi solutions of set optimization problems," Journal of Global Optimization, Springer, vol. 82(3), pages 559-576, March.
    9. F. Rendl, 2016. "Semidefinite relaxations for partitioning, assignment and ordering problems," Annals of Operations Research, Springer, vol. 240(1), pages 119-140, May.
    10. C. Gutiérrez & L. Huerga & V. Novo & C. Tammer, 2016. "Duality related to approximate proper solutions of vector optimization problems," Journal of Global Optimization, Springer, vol. 64(1), pages 117-139, January.
    11. Levent Tunçel & Henry Wolkowicz, 2012. "Strong duality and minimal representations for cone optimization," Computational Optimization and Applications, Springer, vol. 53(2), pages 619-648, October.
    12. T. Q. Son & J. J. Strodiot & V. H. Nguyen, 2009. "ε-Optimality and ε-Lagrangian Duality for a Nonconvex Programming Problem with an Infinite Number of Constraints," Journal of Optimization Theory and Applications, Springer, vol. 141(2), pages 389-409, May.
    13. Hanif Sherali & Evrim Dalkiran & Jitamitra Desai, 2012. "Enhancing RLT-based relaxations for polynomial programming problems via a new class of v-semidefinite cuts," Computational Optimization and Applications, Springer, vol. 52(2), pages 483-506, June.
    14. Zhe Hong & Kwan Deok Bae & Do Sang Kim, 2022. "Minimax programming as a tool for studying robust multi-objective optimization problems," Annals of Operations Research, Springer, vol. 319(2), pages 1589-1606, December.
    15. T. Son & D. Kim, 2013. "ε-Mixed type duality for nonconvex multiobjective programs with an infinite number of constraints," Journal of Global Optimization, Springer, vol. 57(2), pages 447-465, October.
    16. Shaojian Qu & Mark Goh & Soon-Yi Wu & Robert Souza, 2014. "Multiobjective DC programs with infinite convex constraints," Journal of Global Optimization, Springer, vol. 59(1), pages 41-58, May.
    17. Yong Xia & Ying-Wei Han, 2014. "Partial Lagrangian relaxation for the unbalanced orthogonal Procrustes problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 79(2), pages 225-237, April.
    18. Christian Kanzow & Alexandra Schwartz, 2015. "The Price of Inexactness: Convergence Properties of Relaxation Methods for Mathematical Programs with Complementarity Constraints Revisited," Mathematics of Operations Research, INFORMS, vol. 40(2), pages 253-275, February.
    19. P. Kesarwani & P. K. Shukla & J. Dutta & K. Deb, 2022. "Approximations for Pareto and Proper Pareto solutions and their KKT conditions," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 96(1), pages 123-148, August.
    20. Xiangkai Sun & Hongyong Fu & Jing Zeng, 2018. "Robust Approximate Optimality Conditions for Uncertain Nonsmooth Optimization with Infinite Number of Constraints," Mathematics, MDPI, vol. 7(1), pages 1-14, 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:176:y:2018:i:1:d:10.1007_s10957-017-1199-8. 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.