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Second-order KKT optimality conditions for multiobjective discrete optimal control problems

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Abstract

This paper deals with second-order necessary and sufficient optimality conditions of Karush–Kuhn–Tucker-type for local optimal solutions in the sense of Pareto to a class of multi-objective discrete optimal control problems with nonconvex cost functions and state-control constraints. By establishing an abstract result on second-order optimality conditions for a multi-objective mathematical programming problem, we derive second-order necessary and sufficient optimality conditions for a multi-objective 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

The authors would like to thank the referee for careful reading and constructive comments. A part of this work was done while the third author was visiting Vietnam Institute for Advanced Study in Mathematics (VIASM). He would like to thank VIASM for support and hospitality. The research of the fourth author was supported by the National Natural Science Foundation of China (11771067), the Applied Basic Project of Sichuan Province (2019YJ0204) and the Fundamental Research Funds for the Central Universities (ZYGX2019J095).

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Authors and Affiliations

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

    Nguyen Thi Toan & Le Quang Thuy

  2. School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan, People’s Republic of China

    Nguyen Van Tuyen & Yi-Bin Xiao

  3. Department of Mathematics, Hanoi Pedagogical University 2, Xuan Hoa, Phuc Yen, Vinh Phuc, Vietnam

    Nguyen Van Tuyen

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  1. Nguyen Thi Toan
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  2. Le Quang Thuy
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  4. Yi-Bin Xiao
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Correspondence to Nguyen Thi Toan.

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Toan, N.T., Thuy, L.Q., Van Tuyen, N. et al. Second-order KKT optimality conditions for multiobjective discrete optimal control problems . J Glob Optim 79, 203–231 (2021). https://doi.org/10.1007/s10898-020-00935-7

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