The Mordukhovich Coderivative and the Local Metric Regularity of the Solution Map to a Parametric Discrete Optimal Control Problem
In this paper, we study the Mordukhovich coderivative and the local metric regularity in Robinson’s sense of the solution map to a parametric dynamic programming problem with linear constraints and convex cost functions. By establishing abstract results on the coderivative and the local metric regul...
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| Published in: | Acta mathematica vietnamica Vol. 43; no. 1; pp. 175 - 199 |
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| Language: | English |
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01.03.2018
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| Abstract | In this paper, we study the Mordukhovich coderivative and the local metric regularity in Robinson’s sense of the solution map to a parametric dynamic programming problem with linear constraints and convex cost functions. By establishing abstract results on the coderivative and the local metric regularity of the solution map to a parametric variational inequality, we obtain the Mordukhovich coderivative and the local metric regularity in Robinson’s sense of the solution map to a parametric discrete optimal control problem. |
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| AbstractList | In this paper, we study the Mordukhovich coderivative and the local metric regularity in Robinson’s sense of the solution map to a parametric dynamic programming problem with linear constraints and convex cost functions. By establishing abstract results on the coderivative and the local metric regularity of the solution map to a parametric variational inequality, we obtain the Mordukhovich coderivative and the local metric regularity in Robinson’s sense of the solution map to a parametric discrete optimal control problem. |
| Author | Thuy, Le Quang Toan, Nguyen Thi |
| Author_xml | – sequence: 1 givenname: Le Quang surname: Thuy fullname: Thuy, Le Quang organization: School of Applied Mathematics and Informatics, Hanoi University of Science and Technology – sequence: 2 givenname: Nguyen Thi surname: Toan fullname: Toan, Nguyen Thi email: toan.nguyenthi@hust.edu.vn organization: School of Applied Mathematics and Informatics, Hanoi University of Science and Technology |
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| Cites_doi | 10.1287/moor.1040.0133 10.1007/BF00938948 10.1109/TAC.1972.1100010 10.1006/jmaa.1994.1144 10.1016/j.na.2010.06.007 10.1287/moor.21.3.555 10.1007/s10957-014-0648-x 10.1007/s10898-013-0062-1 10.1137/090766413 10.1016/j.na.2008.04.005 10.1137/0325033 10.1007/978-3-642-02431-3 10.1007/s10898-015-0333-0 10.1016/j.jmaa.2011.02.006 10.1007/3-540-31247-1 |
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| Copyright | Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd. 2017 Copyright Springer Science & Business Media 2018 |
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| Keywords | Mordukhovich coderivative 49K21 93C55 49J21 Parametric discrete optimal control problem Solution map Dynamic programming problem Local metric regularity |
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| SubjectTerms | Dynamic programming Mathematics Mathematics and Statistics Optimal control Regularity |
| Title | The Mordukhovich Coderivative and the Local Metric Regularity of the Solution Map to a Parametric Discrete Optimal Control Problem |
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