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The Zero Duality Gap Property for an Optimal Control Problem Governed by a Multivalued Hemivariational Inequality

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Abstract

We show in this work the zero duality gap property for an optimal control problem governed by a multivalued hemivariational inequality with unbounded constraint set. Based on the existence of solutions to the inequality, we establish several sufficient conditions for the zero duality gap property between the optimal control problem and its nonlinear dual problem by using nonlinear Lagrangian methods. Moreover, we obtain a convergence result for the optimal control problem governed by a perturbed multivalued hemivariational inequality.

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Authors and Affiliations

  1. School of Science, Nanjing University of Science and Technology, Nanjing, 210094, Jiangsu, China

    Fengzhen Long

  2. Faculty of Mathematics and Physics, Guangxi University for Nationalities, Nanning, 530006, Guangxi, China

    Biao Zeng

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  1. Fengzhen Long
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  2. Biao Zeng
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Correspondence to Biao Zeng.

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The work is supported by the Natural Science Foundation of Guangxi Province (No. 2019GXNSFBA185005), the Start-up Project of Scientific Research on Introducing talents at school level in Guangxi University for Nationalities (No. 2019KJQD04) and Xiangsihu Young Scholars Innovative Research Team of Guangxi University for Nationalities (No. 2019RSCXSHQN02).

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Long, F., Zeng, B. The Zero Duality Gap Property for an Optimal Control Problem Governed by a Multivalued Hemivariational Inequality. Appl Math Optim 84, 2629–2643 (2021). https://doi.org/10.1007/s00245-020-09721-z

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