A Multilevel Monte Carlo Approach for a Stochastic Optimal Control Problem Based on the Gradient Projection Method
A multilevel Monte Carlo (MLMC) method is applied to simulate a stochastic optimal problem based on the gradient projection method. In the numerical simulation of the stochastic optimal control problem, the approximation of expected value is involved, and the MLMC method is used to address it. The c...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-02-01
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| Series: | AppliedMath |
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| Online Access: | https://www.mdpi.com/2673-9909/3/1/8 |
| _version_ | 1797613788948594688 |
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| author | Changlun Ye Xianbing Luo |
| author_facet | Changlun Ye Xianbing Luo |
| author_sort | Changlun Ye |
| collection | DOAJ |
| description | A multilevel Monte Carlo (MLMC) method is applied to simulate a stochastic optimal problem based on the gradient projection method. In the numerical simulation of the stochastic optimal control problem, the approximation of expected value is involved, and the MLMC method is used to address it. The computational cost of the MLMC method and the convergence analysis of the MLMC gradient projection algorithm are presented. Two numerical examples are carried out to verify the effectiveness of our method. |
| first_indexed | 2024-03-11T06:59:36Z |
| format | Article |
| id | doaj.art-7a9364403e804ac8b9c63817d633d007 |
| institution | Directory Open Access Journal |
| issn | 2673-9909 |
| language | English |
| last_indexed | 2024-03-11T06:59:36Z |
| publishDate | 2023-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | AppliedMath |
| spelling | doaj.art-7a9364403e804ac8b9c63817d633d0072023-11-17T09:20:04ZengMDPI AGAppliedMath2673-99092023-02-01319811610.3390/appliedmath3010008A Multilevel Monte Carlo Approach for a Stochastic Optimal Control Problem Based on the Gradient Projection MethodChanglun Ye0Xianbing Luo1South Huaxi Avenue, School of Mathematics and Statistics, Guizhou University, No. 2708, Guiyang 550025, ChinaSouth Huaxi Avenue, School of Mathematics and Statistics, Guizhou University, No. 2708, Guiyang 550025, ChinaA multilevel Monte Carlo (MLMC) method is applied to simulate a stochastic optimal problem based on the gradient projection method. In the numerical simulation of the stochastic optimal control problem, the approximation of expected value is involved, and the MLMC method is used to address it. The computational cost of the MLMC method and the convergence analysis of the MLMC gradient projection algorithm are presented. Two numerical examples are carried out to verify the effectiveness of our method.https://www.mdpi.com/2673-9909/3/1/8gradient projectionmultilevel Monte Carlostochasticoptimal control problem |
| spellingShingle | Changlun Ye Xianbing Luo A Multilevel Monte Carlo Approach for a Stochastic Optimal Control Problem Based on the Gradient Projection Method AppliedMath gradient projection multilevel Monte Carlo stochastic optimal control problem |
| title | A Multilevel Monte Carlo Approach for a Stochastic Optimal Control Problem Based on the Gradient Projection Method |
| title_full | A Multilevel Monte Carlo Approach for a Stochastic Optimal Control Problem Based on the Gradient Projection Method |
| title_fullStr | A Multilevel Monte Carlo Approach for a Stochastic Optimal Control Problem Based on the Gradient Projection Method |
| title_full_unstemmed | A Multilevel Monte Carlo Approach for a Stochastic Optimal Control Problem Based on the Gradient Projection Method |
| title_short | A Multilevel Monte Carlo Approach for a Stochastic Optimal Control Problem Based on the Gradient Projection Method |
| title_sort | multilevel monte carlo approach for a stochastic optimal control problem based on the gradient projection method |
| topic | gradient projection multilevel Monte Carlo stochastic optimal control problem |
| url | https://www.mdpi.com/2673-9909/3/1/8 |
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