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Acta Mathematica Vietnamica

, Volume 43, Issue 2, pp 201–217 | Cite as

Differential Stability of Convex Discrete Optimal Control Problems

  • Duong Thi Viet An
  • Nguyen Thi Toan
Article

Abstract

Differential stability of convex discrete optimal control problems in Banach spaces is studied in this paper. By using some recent results of An and Yen (Appl. Anal. 94, 108–128, 2015) on differential stability of parametric convex optimization problems under inclusion constraints, we obtain an upper estimate for the subdifferential of the optimal value function of a parametric convex discrete optimal control problem, where the objective function may be nondifferentiable. If the objective function is differentiable, the obtained upper estimate becomes an equality. It is shown that the singular subdifferential of the just mentioned optimal value function always consists of the origin of the dual space.

Keywords

Parametric convex discrete optimal control problem Optimal value function Subdifferentials Linear operator with closed range Adjoint operator 

Mathematics Subject Classification (2010)

93C55 93C73 49K40 49J53 90C31 90C25 

Notes

Acknowledgements

The research of Duong Thi Viet An was supported by the College of Sciences, Thai Nguyen University, Vietnam. The research of Nguyen Thi Toan was supported by the National Foundation for Science and Technology Development (Vietnam) under grant number 101.01-2015.04. The authors thank Professor Nguyen Dong Yen for useful discussions and the anonymous referees for valuable remarks.

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Copyright information

© Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd. 2017

Authors and Affiliations

  1. 1.Department of Mathematics and Informatics, College of SciencesThai Nguyen UniversityThai Nguyen CityVietnam
  2. 2.School of Applied Mathematics and InformaticsHanoi University of Science and TechnologyHanoiVietnam

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