Nonlinear Quasi-hemivariational Inequalities: Existence and Optimal Control

2021 ◽  
Vol 59 (2) ◽  
pp. 1246-1274
Author(s):  
Shengda Zeng ◽  
Stanisław Migórski ◽  
Akhtar A. Khan
Keyword(s):  
Optimal Control ◽  
Hemivariational Inequalities

Convergence analysis of numerical solutions for optimal control of variational–hemivariational inequalities

2020 ◽  
Vol 105 ◽  
pp. 106327
Author(s):  
Danfu Han ◽  
Weimin Han ◽  
Stanisław Migórski ◽  
Junfeng Zhao
Keyword(s):  
Optimal Control ◽  
Convergence Analysis ◽  
Numerical Solutions ◽  
Hemivariational Inequalities

Optimal control of hyperbolic H-hemivariational inequalities with state constraints

2004 ◽  
Vol 25 (7) ◽  
pp. 723-729 ◽  
Author(s):  
Lu Wei-gang ◽  
Guo Xing-ming ◽  
Zhou Shi-xing
Keyword(s):  
Optimal Control ◽  
State Constraints ◽  
Hemivariational Inequalities

scholarly journals Existence and Convergence Results for Generalized Mixed Quasi-Variational Hemivariational Inequality Problem

Symmetry ◽  
2021 ◽  
Vol 13 (10) ◽  
pp. 1882
Author(s):  
Shih-Sen Chang ◽  
Salahuddin ◽  
Lin Wang ◽  
Gang Wang ◽  
Yunhe Zhao
Keyword(s):  
Optimal Control ◽  
Variational Inequality ◽  
Hilbert Spaces ◽  
Hemivariational Inequalities ◽  
Convergence Problem ◽  
The Third ◽  
Convergence Results ◽  
Quasi Variational Inequality ◽  
Existence Of Optimal Control ◽  
The Relationship

The main purpose of this paper is threefold. One is to study the existence and convergence problem of solutions for a class of generalized mixed quasi-variational hemivariational inequalities. The second one is to study the existence of optimal control for such kind of generalized mixed quasi-variational hemivariational inequalities under given control u∈U. The third one is to study the relationship between the optimal control and the data for the underlying generalized mixed quasi-variational inequality problems and a class of minimization problem. As an application, we utilize our results to study the elastic frictional problem in a class of Hilbert spaces. The results presented in the paper extend and improve upon some recent results.

scholarly journals Evolutionary Quasi-Variational-Hemivariational Inequalities I: Existence and Optimal Control

2021 ◽  
Author(s):  
Shengda Zeng ◽  
Dumitru Motreanu ◽  
Akhtar A. Khan
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Variational Problem ◽  
Existence Of Solutions ◽  
Hemivariational Inequalities ◽  
Central Idea ◽  
Monotone Map ◽  
Continuity Properties ◽  
Sequential Compactness

AbstractWe study a nonlinear evolutionary quasi–variational–hemivariational inequality (in short, (QVHVI)) involving a set-valued pseudo-monotone map. The central idea of our approach consists of introducing a parametric variational problem that defines a variational selection associated with (QVHVI). We prove the solvability of the parametric variational problem by employing a surjectivity theorem for the sum of operators, combined with Minty’s formulation and techniques from the nonsmooth analysis. Then, an existence theorem for (QVHVI) is established by using Kluge’s fixed point theorem for set-valued operators. As an application, an abstract optimal control problem for the (QVHVI) is investigated. We prove the existence of solutions for the optimal control problem and the weak sequential compactness of the solution set via the Weierstrass minimization theorem and the Kuratowski-type continuity properties.

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