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Mathematics
Volume 11
Issue 18
10.3390/math11183885
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Article

Quantitative Stability of Optimization Problems with Stochastic Constraints

by
Wei Ouyang
*,† and
Kui Mei
School of Mathematics, Yunnan Normal University, Kunming 650500, China
*
Author to whom correspondence should be addressed.
†
Current address: Yunnan Key Laboratory of Modern Analytical Mathematics and Applications, Kunming 650500, China.
Mathematics 2023, 11(18), 3885; https://doi.org/10.3390/math11183885
Submission received: 9 August 2023 / Revised: 8 September 2023 / Accepted: 11 September 2023 / Published: 12 September 2023
Versions Notes

Abstract

In this paper, we consider optimization problems with stochastic constraints. We derive quantitative stability results for the optimal value function, the optimal solution set and the feasible solution set of optimization models in which the underlying stochastic constraints involve the mathematical expectation of random single-valued and set-valued mappings, respectively. New primal sufficient conditions are developed for the uniform error bound property of the stochastic constraint system for the single-valued case.
Keywords: stochastic generalized equation; quantitative stability; uniform error bound; metric regularity stochastic generalized equation; quantitative stability; uniform error bound; metric regularity

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MDPI and ACS Style

Ouyang, W.; Mei, K. Quantitative Stability of Optimization Problems with Stochastic Constraints. Mathematics 2023, 11, 3885. https://doi.org/10.3390/math11183885

AMA Style

Ouyang W, Mei K. Quantitative Stability of Optimization Problems with Stochastic Constraints. Mathematics. 2023; 11(18):3885. https://doi.org/10.3390/math11183885

Chicago/Turabian Style

Ouyang, Wei, and Kui Mei. 2023. "Quantitative Stability of Optimization Problems with Stochastic Constraints" Mathematics 11, no. 18: 3885. https://doi.org/10.3390/math11183885

APA Style

Ouyang, W., & Mei, K. (2023). Quantitative Stability of Optimization Problems with Stochastic Constraints. Mathematics, 11(18), 3885. https://doi.org/10.3390/math11183885

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