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A stochastic primal-dual method for a class of nonconvex constrained optimization

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Listed:
  • Lingzi Jin

    (University of Chinese Academy of Sciences
    Peng Cheng Laboratory)

  • Xiao Wang

    (University of Chinese Academy of Sciences
    Peng Cheng Laboratory)

Abstract

In this paper we study a class of nonconvex optimization which involves uncertainty in the objective and a large number of nonconvex functional constraints. Challenges often arise when solving this type of problems due to the nonconvexity of the feasible set and the high cost of calculating function value and gradient of all constraints simultaneously. To handle these issues, we propose a stochastic primal-dual method in this paper. At each iteration, a proximal subproblem based on a stochastic approximation to an augmented Lagrangian function is solved to update the primal variable, which is then used to update dual variables. We explore theoretical properties of the proposed algorithm and establish its iteration and sample complexities to find an $$\epsilon$$ ϵ -stationary point of the original problem. Numerical tests on a weighted maximin dispersion problem and a nonconvex quadratically constrained optimization problem demonstrate the promising performance of the proposed algorithm.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:coopap:v:83:y:2022:i:1:d:10.1007_s10589-022-00384-w
    DOI: 10.1007/s10589-022-00384-w
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    References listed on IDEAS

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    1. Raffaello Seri & Christine Choirat, 2013. "Scenario Approximation of Robust and Chance-Constrained Programs," Journal of Optimization Theory and Applications, Springer, vol. 158(2), pages 590-614, August.
    2. Weiwei Pan & Jingjing Shen & Zi Xu, 2021. "An efficient algorithm for nonconvex-linear minimax optimization problem and its application in solving weighted maximin dispersion problem," Computational Optimization and Applications, Springer, vol. 78(1), pages 287-306, January.
    3. M. C. Campi & S. Garatti, 2011. "A Sampling-and-Discarding Approach to Chance-Constrained Optimization: Feasibility and Optimality," Journal of Optimization Theory and Applications, Springer, vol. 148(2), pages 257-280, February.
    4. 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.
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    Cited by:

    1. Rulei Qi & Dan Xue & Yujia Zhai, 2024. "A Momentum-Based Adaptive Primal–Dual Stochastic Gradient Method for Non-Convex Programs with Expectation Constraints," Mathematics, MDPI, vol. 12(15), pages 1-26, July.
    2. Zichong Li & Pin-Yu Chen & Sijia Liu & Songtao Lu & Yangyang Xu, 2024. "Stochastic inexact augmented Lagrangian method for nonconvex expectation constrained optimization," Computational Optimization and Applications, Springer, vol. 87(1), pages 117-147, January.

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