The Mordukhovich Coderivative and the Local Metric Regularity of the Solution Map to a Parametric Discrete Optimal Control Problem

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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Acknowledgements

This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 101.01-2015.04 and by the Vietnam Institute for Advanced Study in Mathematics (VIASM).

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Correspondence to Nguyen Thi Toan.

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Thuy, L.Q., Toan, N.T. The Mordukhovich Coderivative and the Local Metric Regularity of the Solution Map to a Parametric Discrete Optimal Control Problem. Acta Math Vietnam 43, 175–199 (2018). https://doi.org/10.1007/s40306-017-0224-1

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Keywords

  • Parametric discrete optimal control problem
  • Dynamic programming problem
  • Solution map
  • Local metric regularity
  • Mordukhovich coderivative

Mathematics Subject Classification (2010)

  • 49J21
  • 49K21
  • 93C55