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Well-Posedness, Optimal Control, and Sensitivity Analysis for a Class of Differential Variational-Hemivariational Inequalities

Authors:

Stanisław Migórski,

Zhenhai LiuAuthors Info & Claims

SIAM Journal on Optimization, Volume 31, Issue 4

Pages 2829 - 2862

https://doi.org/10.1137/20M1351436

Published: 01 January 2021 Publication History

Abstract

The objective of the paper is to investigate a dynamical system called a differential variational-hemivariational inequality (DVHVI) which couples an abstract variational-hemivariational inequality of elliptic type and a nonlinear evolution inclusion problem in a Banach space. Under appropriate assumptions, the nonemptiness and compactness of the solution set for DVHVI are established by using the Fan--Knaster--Kuratowski--Mazurkiewicz principle, the Minty approach, and the methods of nonsmooth analysis. Then, we explore properties of solution mapping for DVHVI which involve the relative compactness, continuity, and convergence in the Kuratowski sense. Employing these properties, we prove existence of a solution to the optimal control problem driven by a DVHVI. Next, well-posedness results for DVHVI are obtained, including the existence, uniqueness, and stability of the solution. Furthermore, we study sensitivity of a perturbed problem with multiparameters corresponding to DVHVI. Finally, a comprehensive parabolic-elliptic system with obstacle effect is considered as an illustrative application.

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Cited By

Van Anh NVan Thuy T(2024)Long-time behavior of delay differential quasi-variational–hemivariational inequalities and application to contact problemsZeitschrift für Angewandte Mathematik und Physik (ZAMP)10.1007/s00033-024-02202-175:2Online publication date: 1-Apr-2024
https://dl.acm.org/doi/10.1007/s00033-024-02202-1
Zhang XLu YLiu D(2023)Stability and Optimal Controls for Time-space Fractional Ginzburg–Landau SystemsJournal of Optimization Theory and Applications10.1007/s10957-023-02315-z199:3(1106-1129)Online publication date: 1-Dec-2023
https://dl.acm.org/doi/10.1007/s10957-023-02315-z
Liu CYu CGong ZCheong HTeo K(2023)Numerical Computation of Optimal Control Problems with Atangana–Baleanu Fractional DerivativesJournal of Optimization Theory and Applications10.1007/s10957-023-02212-5197:2(798-816)Online publication date: 8-Apr-2023
https://dl.acm.org/doi/10.1007/s10957-023-02212-5
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cover image SIAM Journal on Optimization

SIAM Journal on Optimization Volume 31, Issue 4

DOI:10.1137/sjope8.31.4

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© 2021, Society for Industrial and Applied Mathematics.

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Society for Industrial and Applied Mathematics

United States

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Published: 01 January 2021

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Cited By

Van Anh NVan Thuy T(2024)Long-time behavior of delay differential quasi-variational–hemivariational inequalities and application to contact problemsZeitschrift für Angewandte Mathematik und Physik (ZAMP)10.1007/s00033-024-02202-175:2Online publication date: 1-Apr-2024
https://dl.acm.org/doi/10.1007/s00033-024-02202-1
Zhang XLu YLiu D(2023)Stability and Optimal Controls for Time-space Fractional Ginzburg–Landau SystemsJournal of Optimization Theory and Applications10.1007/s10957-023-02315-z199:3(1106-1129)Online publication date: 1-Dec-2023
https://dl.acm.org/doi/10.1007/s10957-023-02315-z
Liu CYu CGong ZCheong HTeo K(2023)Numerical Computation of Optimal Control Problems with Atangana–Baleanu Fractional DerivativesJournal of Optimization Theory and Applications10.1007/s10957-023-02212-5197:2(798-816)Online publication date: 8-Apr-2023
https://dl.acm.org/doi/10.1007/s10957-023-02212-5
Migórski SCai D(2023)A New System of Differential Quasi-Hemivariational Inequalities in Contact MechanicsApplied Mathematics and Optimization10.1007/s00245-023-09991-388:1Online publication date: 25-Apr-2023
https://dl.acm.org/doi/10.1007/s00245-023-09991-3
Liu JYang XZeng SZhao Y(2022)Coupled Variational Inequalities: Existence, Stability and Optimal ControlJournal of Optimization Theory and Applications10.1007/s10957-021-01995-9193:1-3(877-909)Online publication date: 1-Jun-2022
https://dl.acm.org/doi/10.1007/s10957-021-01995-9
Cen JHaddad TNguyen VZeng S(2022)Simultaneous distributed-boundary optimal control problems driven by nonlinear complementarity systemsJournal of Global Optimization10.1007/s10898-022-01155-x84:3(783-805)Online publication date: 1-Nov-2022
https://dl.acm.org/doi/10.1007/s10898-022-01155-x
Zeng SMigórski STarzia DZou LNguyen V(2022)A class of elliptic mixed boundary value problems with (p, q)-Laplacian: existence, comparison and optimal controlZeitschrift für Angewandte Mathematik und Physik (ZAMP)10.1007/s00033-022-01789-773:4Online publication date: 1-Aug-2022
https://dl.acm.org/doi/10.1007/s00033-022-01789-7

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