Affiliation:
1. School of Mathematical Sciences, Dalian University of Technology, 116024 Dalian, China;
2. School of Science, Dalian Maritime University, 116026 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 [Formula: see text] 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 [Formula: see text] constraint violation bound and [Formula: see text] objective bound. Numerical results demonstrate that the proposed algorithm is efficient. History: Accepted byAntonio Frangioni, Area Editor for Design & Analysis ofAlgorithms—Continuous. Funding: This work was supported by the National Natural Science Foundation of China [Grants 11971089, 11731013, 12071055, and 11871135]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplementary Information [ https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.1228 ] or is available from the IJOC GitHub software repository ( https://github.com/INFORMSJoC ) at http://dx.doi.org/10.5281/zenodo.6818229 .
Publisher
Institute for Operations Research and the Management Sciences (INFORMS)
Cited by
1 articles.
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