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On the No-Gap Second-Order Optimality Conditions for a Discrete Optimal Control Problem with Mixed Constraints

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Abstract

Motivated by our recent works on optimality conditions in discrete optimal control problems under a nonconvex cost function, in this paper, we study second-order necessary and sufficient optimality conditions for a discrete optimal control problem with a nonconvex cost function and state-control constraints. By establishing an abstract result on second-order optimality conditions for a mathematical programming problem, we derive second-order necessary and sufficient optimality conditions for a discrete optimal control problem. Using a common critical cone for both the second-order necessary and sufficient optimality conditions, we obtain “no-gap” between second-order optimality conditions.

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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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Authors and Affiliations

  1. School of Applied Mathematics and Informatics, Hanoi University of Science and Technology, 1 Dai Co Viet, Hanoi, Vietnam

    Le Quang Thuy & Nguyen Thi Toan

  2. Department of Fundamental, Nghe An College of Economics, 51 Ly Tu Trong, Vinh City, Vietnam

    Bui Thi Thanh

Authors
  1. Le Quang Thuy
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  2. Bui Thi Thanh
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  3. Nguyen Thi Toan
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Correspondence to Nguyen Thi Toan.

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Communicated by Boris S. Mordukhovich.

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Thuy, L.Q., Thanh, B.T. & Toan, N.T. On the No-Gap Second-Order Optimality Conditions for a Discrete Optimal Control Problem with Mixed Constraints. J Optim Theory Appl 173, 421–442 (2017). https://doi.org/10.1007/s10957-017-1094-3

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  • DOI: https://doi.org/10.1007/s10957-017-1094-3

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