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Lagrangian methods for optimal control problems governed by a mixed quasi-variational inequality

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Abstract

This paper studies an optimal control problem where the state of the system is defined by a mixed quasi-variational inequality. Several sufficient conditions for the zero duality gap property between the optimal control problem and its nonlinear dual problem are obtained by using nonlinear Lagrangian methods. Our results are applied to an example where the mixed quasi-variational inequality leads to a bilateral obstacle problem.

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Acknowledgements

The authors are grateful to the editor and the referees for their valuable comments and suggestions. Z. Wang is supported by the fundamental research funds for the central universities (2682015CX061), the NSF of China (Tianyuan funds for Mathematics, no. 11526170); Z.Y. Chen is supported by the NSF of China (Tianyuan funds for Mathematics, no. 11526169) and the fundamental research funds for the central universities (2682017CX062).

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Authors and Affiliations

  1. Department of Mathematics, Southwest Jiaotong University, Chengdu, 611756, Sichuan, People’s Republic of China

    Zhong-bao Wang, Zi-li Chen & Zhang-you Chen

  2. Department of Mathematics, Kunming University, Kunming, 650221, Yunnan, People’s Republic of China

    Si-sheng Yao

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  1. Zhong-bao Wang
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  2. Zi-li Chen
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  3. Zhang-you Chen
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  4. Si-sheng Yao
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Correspondence to Zhang-you Chen.

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Wang, Zb., Chen, Zl., Chen, Zy. et al. Lagrangian methods for optimal control problems governed by a mixed quasi-variational inequality. Optim Lett 12, 1357–1371 (2018). https://doi.org/10.1007/s11590-017-1179-9

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  • DOI: https://doi.org/10.1007/s11590-017-1179-9

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