Necessary optimality conditions for local minimizers of stochastic optimal control problems with state constraints
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- by Hélène Frankowska, Haisen Zhang and Xu Zhang PDF
- Trans. Amer. Math. Soc. 372 (2019), 1289-1331 Request permission
Abstract:
The main purpose of this work is to establish some first- and second-order necessary optimality conditions for local minimizers of stochastic optimal control problems with state constraints. The control may affect both the drift and the diffusion terms of the systems, and the control regions are allowed to be nonconvex. A stochastic inward pointing condition is proposed to ensure the normality of the corresponding necessary conditions.References
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Additional Information
- Hélène Frankowska
- Affiliation: CNRS, IMJ-PRG, Sorbonne Université, case 247, 4 place Jussieu, 75252 Paris, France
- Email: helene.frankowska@imj-prg.fr.
- Haisen Zhang
- Affiliation: School of Mathematical Sciences, Sichuan Normal University, Chengdu 610066, People’s Republic of China; and School of Mathematical Sciences, Southwest University, Chongqing, 400715, People’s Republic of China and CNRS, IMJ-PRG, Sorbonne Université, case 247, 4 place Jussieu, 75252 Paris, France
- MR Author ID: 1047103
- Email: haisenzhang@yeah.net
- Xu Zhang
- Affiliation: School of Mathematics, Sichuan University, Chengdu 610064, People’s Republic of China
- MR Author ID: 636278
- Email: zhang_xu@scu.edu.cn
- Received by editor(s): November 6, 2017
- Received by editor(s) in revised form: May 15, 2018
- Published electronically: April 18, 2019
- Additional Notes: The research of the first author benefited from the support of the “FMJH Program Gaspard Monge in optimization and operation research”, and from the support to this program from EDF under grant PGMO 2016-2832H and CNRS-NSFC PRC Project under grant 271392.
The research of the second author is partially supported by NSF of China under grant 11701470, the State Scholarship Fund of China Scholarship Council under grant [2016]3035 and the NSF of CQ CSTC under grant 2015jcyjA00017 and the Advance and Basic Research Project of Chongqing under grant cstc2016jcyjA0239.
The research of the third author is partially supported by NSF of China under grants 11221101 and 11231007, the NSFC-CNRS Joint Research Project under grant 11711530142, the PCSIRT under grant IRT_16R53 and the Chang Jiang Scholars Program from the Chinese Education Ministry. - © Copyright 2019 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 372 (2019), 1289-1331
- MSC (2010): Primary 93E20; Secondary 49J53, 60H10
- DOI: https://doi.org/10.1090/tran/7669
- MathSciNet review: 3968803