IDEAS home Printed from https://ideas.repec.org/a/inm/ormoor/v48y2023i1p177-193.html
   My bibliography  Save this article

Stochastic Approximation Proximal Method of Multipliers for Convex Stochastic Programming

Author

Listed:
  • Liwei Zhang

    (Institute of Operations Research and Control Theory, School of Mathematical Sciences, Dalian University of Technology, 116023 Dalian, China)

  • Yule Zhang

    (Department of Statistics, School of Science, Dalian Maritime University, 116026 Dalian, China)

  • Xiantao Xiao

    (Institute of Operations Research and Control Theory, School of Mathematical Sciences, Dalian University of Technology, 116023 Dalian, China)

  • Jia Wu

    (Institute of Operations Research and Control Theory, School of Mathematical Sciences, Dalian University of Technology, 116023 Dalian, China)

Abstract

This paper considers the problem of minimizing a convex expectation function over a closed convex set, coupled with a set of inequality convex expectation constraints. We present a new stochastic approximation proximal method of multipliers to solve this convex stochastic optimization problem. We analyze regrets of the proposed method for solving convex stochastic optimization problems. Under mild conditions, we show that this method exhibits sublinear regret for both objective reduction and constraint violation if parameters in the algorithm are properly chosen. Moreover, we investigate the high probability performance of the proposed method under the standard light-tail assumption.

Suggested Citation

  • Liwei Zhang & Yule Zhang & Xiantao Xiao & Jia Wu, 2023. "Stochastic Approximation Proximal Method of Multipliers for Convex Stochastic Programming," Mathematics of Operations Research, INFORMS, vol. 48(1), pages 177-193, February.
    • Handle: RePEc:inm:ormoor:v:48:y:2023:i:1:p:177-193
    DOI: 10.1287/moor.2022.1257
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/moor.2022.1257
    Download Restriction: no
    File URL: https://libkey.io/10.1287/moor.2022.1257?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
    ---><---

    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:inm:ormoor:v:48:y:2023:i:1:p:177-193. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    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.