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Solving Stochastic Optimization with Expectation Constraints Efficiently by a Stochastic Augmented Lagrangian-Type Algorithm

Author

Listed:
  • Liwei Zhang

    (School of Mathematical Sciences, Dalian University of Technology, 116024 Dalian, China)

  • Yule Zhang

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

  • Jia Wu

    (School of Mathematical Sciences, Dalian University of Technology, 116024 Dalian, China)

  • Xiantao Xiao

    (School of Mathematical Sciences, Dalian University of Technology, 116024 Dalian, China)

Abstract

This paper considers the problem of minimizing a convex expectation function with a set of inequality convex expectation constraints. We propose a stochastic augmented Lagrangian-type algorithm—namely, the stochastic linearized proximal method of multipliers—to solve this convex stochastic optimization problem. This algorithm can be roughly viewed as a hybrid of stochastic approximation and the traditional proximal method of multipliers. Under mild conditions, we show that this algorithm exhibits O ( K − 1 / 2 ) expected convergence rates for both objective reduction and constraint violation if parameters in the algorithm are properly chosen, where K denotes the number of iterations. Moreover, we show that, with high probability, the algorithm has a O ( log ( K ) K − 1 / 2 ) constraint violation bound and O ( log 3 / 2 ( K ) K − 1 / 2 ) objective bound. Numerical results demonstrate that the proposed algorithm is efficient.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:orijoc:v:34:y:2022:i:6:p:2989-3006
    DOI: 10.1287/ijoc.2022.1228
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    References listed on IDEAS

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    2. Neslihan Fidan Keçeci & Viktor Kuzmenko & Stan Uryasev, 2016. "Portfolios Dominating Indices: Optimization with Second-Order Stochastic Dominance Constraints vs. Minimum and Mean Variance Portfolios," JRFM, MDPI, vol. 9(4), pages 1-14, October.
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