Expected Residual Minimization Method for a Class of Stochastic Quasivariational Inequality Problems
We consider the expected residual minimization method for a class of stochastic quasivariational inequality problems (SQVIP). The regularized gap function for quasivariational inequality problem (QVIP) is in general not differentiable. We first show that the regularized gap function is differentiabl...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/816528 |
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| author | Hui-Qiang Ma Nan-Jing Huang |
| author_facet | Hui-Qiang Ma Nan-Jing Huang |
| author_sort | Hui-Qiang Ma |
| collection | DOAJ |
| description | We consider the expected residual minimization method for a class of stochastic quasivariational inequality problems (SQVIP). The regularized gap function for quasivariational inequality problem (QVIP) is in general not differentiable. We first show that the regularized gap function is differentiable and convex for a class of QVIPs under some suitable conditions. Then, we reformulate SQVIP as a deterministic minimization problem that minimizes the expected residual of the regularized gap function and solve it by sample average approximation (SAA) method. Finally, we investigate the limiting behavior of the optimal solutions and stationary points. |
| format | Article |
| id | doaj-art-4d1356126d17417bb3a98e1800a079ac |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-4d1356126d17417bb3a98e1800a079ac2025-02-03T05:55:18ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/816528816528Expected Residual Minimization Method for a Class of Stochastic Quasivariational Inequality ProblemsHui-Qiang Ma0Nan-Jing Huang1Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, ChinaDepartment of Mathematics, Sichuan University, Chengdu, Sichuan 610064, ChinaWe consider the expected residual minimization method for a class of stochastic quasivariational inequality problems (SQVIP). The regularized gap function for quasivariational inequality problem (QVIP) is in general not differentiable. We first show that the regularized gap function is differentiable and convex for a class of QVIPs under some suitable conditions. Then, we reformulate SQVIP as a deterministic minimization problem that minimizes the expected residual of the regularized gap function and solve it by sample average approximation (SAA) method. Finally, we investigate the limiting behavior of the optimal solutions and stationary points.http://dx.doi.org/10.1155/2012/816528 |
| spellingShingle | Hui-Qiang Ma Nan-Jing Huang Expected Residual Minimization Method for a Class of Stochastic Quasivariational Inequality Problems Journal of Applied Mathematics |
| title | Expected Residual Minimization Method for a Class of Stochastic Quasivariational Inequality Problems |
| title_full | Expected Residual Minimization Method for a Class of Stochastic Quasivariational Inequality Problems |
| title_fullStr | Expected Residual Minimization Method for a Class of Stochastic Quasivariational Inequality Problems |
| title_full_unstemmed | Expected Residual Minimization Method for a Class of Stochastic Quasivariational Inequality Problems |
| title_short | Expected Residual Minimization Method for a Class of Stochastic Quasivariational Inequality Problems |
| title_sort | expected residual minimization method for a class of stochastic quasivariational inequality problems |
| url | http://dx.doi.org/10.1155/2012/816528 |
| work_keys_str_mv | AT huiqiangma expectedresidualminimizationmethodforaclassofstochasticquasivariationalinequalityproblems AT nanjinghuang expectedresidualminimizationmethodforaclassofstochasticquasivariationalinequalityproblems |