IDEAS home Printed from https://ideas.repec.org/a/spr/coopap/v76y2020i2d10.1007_s10589-020-00179-x.html
   My bibliography  Save this article

Algorithms for stochastic optimization with function or expectation constraints

Author

Listed:
  • Guanghui Lan

    (Georgia Institute of Technology)

  • Zhiqiang Zhou

    (Georgia Institute of Technology)

Abstract

This paper considers the problem of minimizing an expectation function over a closed convex set, coupled with a function or expectation constraint on either decision variables or problem parameters. We first present a new stochastic approximation (SA) type algorithm, namely the cooperative SA (CSA), to handle problems with the constraint on devision variables. We show that this algorithm exhibits the optimal $${{{\mathcal {O}}}}(1/\epsilon ^2)$$O(1/ϵ2) rate of convergence, in terms of both optimality gap and constraint violation, when the objective and constraint functions are generally convex, where $$\epsilon$$ϵ denotes the optimality gap and infeasibility. Moreover, we show that this rate of convergence can be improved to $${{{\mathcal {O}}}}(1/\epsilon )$$O(1/ϵ) if the objective and constraint functions are strongly convex. We then present a variant of CSA, namely the cooperative stochastic parameter approximation (CSPA) algorithm, to deal with the situation when the constraint is defined over problem parameters and show that it exhibits similar optimal rate of convergence to CSA. It is worth noting that CSA and CSPA are primal methods which do not require the iterations on the dual space and/or the estimation on the size of the dual variables. To the best of our knowledge, this is the first time that such optimal SA methods for solving function or expectation constrained stochastic optimization are presented in the literature.

Suggested Citation

  • Guanghui Lan & Zhiqiang Zhou, 2020. "Algorithms for stochastic optimization with function or expectation constraints," Computational Optimization and Applications, Springer, vol. 76(2), pages 461-498, June.
  • Handle: RePEc:spr:coopap:v:76:y:2020:i:2:d:10.1007_s10589-020-00179-x
    DOI: 10.1007/s10589-020-00179-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10589-020-00179-x
    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/s10589-020-00179-x?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. D. Goldfarb & G. Iyengar, 2003. "Robust Portfolio Selection Problems," Mathematics of Operations Research, INFORMS, vol. 28(1), pages 1-38, February.
    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. Lingzi Jin & Xiao Wang, 2022. "A stochastic primal-dual method for a class of nonconvex constrained optimization," Computational Optimization and Applications, Springer, vol. 83(1), pages 143-180, September.
    2. Liwei Zhang & Yule Zhang & Jia Wu & Xiantao Xiao, 2022. "Solving Stochastic Optimization with Expectation Constraints Efficiently by a Stochastic Augmented Lagrangian-Type Algorithm," INFORMS Journal on Computing, INFORMS, vol. 34(6), pages 2989-3006, November.
    3. Li, Bingkang & Zhao, Huiru & Wang, Xuejie & Zhao, Yihang & Zhang, Yuanyuan & Lu, Hao & Wang, Yuwei, 2022. "Distributionally robust offering strategy of the aggregator integrating renewable energy generator and energy storage considering uncertainty and connections between the mid-to-long-term and spot elec," Renewable Energy, Elsevier, vol. 201(P1), pages 400-417.
    4. Yuanyuan, Zhang & Huiru, Zhao & Bingkang, Li, 2023. "Distributionally robust comprehensive declaration strategy of virtual power plant participating in the power market considering flexible ramping product and uncertainties," Applied Energy, Elsevier, vol. 343(C).
    5. Bo Wei & William B. Haskell & Sixiang Zhao, 2020. "The CoMirror algorithm with random constraint sampling for convex semi-infinite programming," Annals of Operations Research, Springer, vol. 295(2), pages 809-841, December.
    6. Drew P. Kouri & Mathias Staudigl & Thomas M. Surowiec, 2023. "A relaxation-based probabilistic approach for PDE-constrained optimization under uncertainty with pointwise state constraints," Computational Optimization and Applications, Springer, vol. 85(2), pages 441-478, June.

    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. Nathan Lassance & Victor DeMiguel & Frédéric Vrins, 2022. "Optimal Portfolio Diversification via Independent Component Analysis," Operations Research, INFORMS, vol. 70(1), pages 55-72, January.
    2. Vaughn Gambeta & Roy Kwon, 2020. "Risk Return Trade-Off in Relaxed Risk Parity Portfolio Optimization," JRFM, MDPI, vol. 13(10), pages 1-28, October.
    3. Maillet, Bertrand & Tokpavi, Sessi & Vaucher, Benoit, 2015. "Global minimum variance portfolio optimisation under some model risk: A robust regression-based approach," European Journal of Operational Research, Elsevier, vol. 244(1), pages 289-299.
    4. Kang, Yan-li & Tian, Jing-Song & Chen, Chen & Zhao, Gui-Yu & Li, Yuan-fu & Wei, Yu, 2021. "Entropy based robust portfolio," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 583(C).
    5. Juan F. Monge & Mercedes Landete & Jos'e L. Ruiz, 2016. "Sharpe portfolio using a cross-efficiency evaluation," Papers 1610.00937, arXiv.org, revised Oct 2016.
    6. Victor DeMiguel & Francisco J. Nogales, 2009. "Portfolio Selection with Robust Estimation," Operations Research, INFORMS, vol. 57(3), pages 560-577, June.
    7. Hakan Kaya, 2017. "Managing ambiguity in asset allocation," Journal of Asset Management, Palgrave Macmillan, vol. 18(3), pages 163-187, May.
    8. Jules Sadefo-Kamdem, 2011. "Downside Risk And Kappa Index Of Non-Gaussian Portfolio With Lpm," Working Papers hal-00733043, HAL.
    9. Man Yiu Tsang & Tony Sit & Hoi Ying Wong, 2022. "Adaptive Robust Online Portfolio Selection," Papers 2206.01064, arXiv.org.
    10. Taozeng Zhu & Jingui Xie & Melvyn Sim, 2022. "Joint Estimation and Robustness Optimization," Management Science, INFORMS, vol. 68(3), pages 1659-1677, March.
    11. Takafumi Kanamori & Akiko Takeda, 2012. "Worst-Case Violation of Sampled Convex Programs for Optimization with Uncertainty," Journal of Optimization Theory and Applications, Springer, vol. 152(1), pages 171-197, January.
    12. Mainik, Georg & Mitov, Georgi & Rüschendorf, Ludger, 2015. "Portfolio optimization for heavy-tailed assets: Extreme Risk Index vs. Markowitz," Journal of Empirical Finance, Elsevier, vol. 32(C), pages 115-134.
    13. Fernando Ordóñez & Nicolás E. Stier-Moses, 2010. "Wardrop Equilibria with Risk-Averse Users," Transportation Science, INFORMS, vol. 44(1), pages 63-86, February.
    14. Paul Glasserman & Wanmo Kang, 2014. "OR Forum—Design of Risk Weights," Operations Research, INFORMS, vol. 62(6), pages 1204-1220, December.
    15. L. Jeff Hong & Zhiyuan Huang & Henry Lam, 2021. "Learning-Based Robust Optimization: Procedures and Statistical Guarantees," Management Science, INFORMS, vol. 67(6), pages 3447-3467, June.
    16. Jang Ho Kim & Woo Chang Kim & Frank J. Fabozzi, 2017. "Penalizing variances for higher dependency on factors," Quantitative Finance, Taylor & Francis Journals, vol. 17(4), pages 479-489, April.
    17. Fonseca, Raquel J. & Rustem, Berç, 2012. "International portfolio management with affine policies," European Journal of Operational Research, Elsevier, vol. 223(1), pages 177-187.
    18. Geng Deng & Tim Dulaney & Craig McCann & Olivia Wang, 2013. "Robust portfolio optimization with Value-at-Risk-adjusted Sharpe ratios," Journal of Asset Management, Palgrave Macmillan, vol. 14(5), pages 293-305, October.
    19. Ben-Tal, A. & den Hertog, D. & De Waegenaere, A.M.B. & Melenberg, B. & Rennen, G., 2011. "Robust Solutions of Optimization Problems Affected by Uncertain Probabilities," Other publications TiSEM 4d43dc51-86d9-4804-8563-9, Tilburg University, School of Economics and Management.
    20. Georg Mainik & Georgi Mitov & Ludger Ruschendorf, 2015. "Portfolio optimization for heavy-tailed assets: Extreme Risk Index vs. Markowitz," Papers 1505.04045, arXiv.org.

    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:coopap:v:76:y:2020:i:2:d:10.1007_s10589-020-00179-x. 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.