This archive is distributed in association with the INFORMS Journal on Computing under the MIT License.

The software and data in this repository are a snapshot of the software and data that were used in the research reported on in the paper Solving Stochastic Optimization with Expectation Constraints Efficiently by a Stochastic Augmented Lagrangian-Type Algorithm by L. Zhang, Y. Zhang, J. Wu and X. Xiao.

To cite this material, please cite this repository, using the following DOI: https://doi.org/10.1287/ijoc.2022.1228.cd

Below is the BibTex for citing this version of the code.

@article{SLPMM2022,
  author =        {Liwei Zhang, Yule Zhang, Jia Wu and Xiantao Xiao},
  publisher =     {INFORMS Journal on Computing},
  title =         {{SLPMM} Version v2021.0248},
  year =          {2022},
  doi =           {10.1287/ijoc.2022.1228.cd},
  url =           {https://github.com/INFORMSJoC/2021.0248},
}  

The goal of this software is to compare the performance of stochastic linearized proximal method of multipliers (SLPMM) proposed in the paper with several existing algorithms for minimizing a convex expectation function subject to a set of inequality convex expectation constraints. A preprint of this paper is available on arXiv.

Three numerical examples are tested in this software:

• Neyman-Pearson classification.
• Stochastic quadratically constrained quadratic programming (QCQP).
• Second-order stochastic dominance (SSD) constrained portfolio optimization.

This software contains three folders: NP_classification, QCQP, SSD.

• NP_classification: solves Neyman-Pearson classification problems.
• QCQP: solves stochastic quadratically constrained quadratic programs.
• SSD: solves second-order stochastic dominance (SSD) constrained portfolio optimization problems.

The compared existing algorithms include:

• CSA: Lan G, Zhou Z (2020) Algorithms for stochastic optimization with function or expectation constraints. Comput. Optim. Appl. 76(2):461–498. link
• YNW: Yu H, Neely MJ, Wei X (2017) Online convex optimization with stochastic constraints. Advances in Neural Information Processing Systems, 1428–1438. link
• PSG: Xiao X (2019) Penalized stochastic gradient methods for stochastic convex optimization with expectation constraints, optimization-online. link
• APriD: Yan Y, Xu Y (2022) Adaptive primal-dual stochastic gradient method for expectation-constrained convex stochastic programs. Math. Program. Comput. 14(2):319–363. link
• PALEM: Dentcheva D, Martinez G, Wolfhagen E (2016) Augmented Lagrangian methods for solving optimization problems with stochastic-order constraints. Oper. Res. 64(6):1451–1465. link

The results in the paper were generated by this software that had been carried out using MATLAB R2020a on a desktop computer with Intel(R) Xeon(R) E-2124G 3.40GHz and 32GB memory. The MATLAB function refline is required which is available in the Statistics Toolbox of MATLAB.

1. The files in folder NP_classification/results show the results of comparison between CSA, YNW, PSG, APriD and SLPMM for Neyman-Pearson classification.

• Figure 1 in the paper shows the results of comparison of algorithms on dataset gisette.
• Figure 2 in the paper shows the results of comparison of algorithms on dataset CINA.
• Figure 3 in the paper shows the results of comparison of algorithms on dataset MNIST.

2. The files in folder QCQP/results show the results of comparison between YNW, PSG, APriD and SLPMM for stochastic quadratically constrained quadratic programming.

• Figure 4 in the paper shows the results of comparison of algorithms on stochastic quadratically constrained quadratic programming.

3. The files in folder SSD/results show the results of comparison between YNW, PSG, APriD, PALEM and SLPMM for SSD constrained portfolio optimization.

• Figure 5 in the paper shows the results of comparison of algorithms on SSD constrained portfolio optimization.

• To replicate the results in Figure 1-3, run the NP_classification/test_NP_classification_logloss.m script.
• To replicate the results in Figure 4, run the QCQP/test_QCQP.m script.
• To replicate the results in Figure 5, run the SSD/test_portfolio_SSD.m script (run SSD/mex_x.m first).

The elapsed cpu time of the experiments is much longer than that is shown in the figures (pure time of the algorithms). The reason is that we have to track the true values of objective and constraint functions at each iteration to show the performance of the algorithms, thus the code is very time-consuming. Each pure time shown in the figures equals to the total time minus the time for computing the true values of objective and constraint functions.