quasi variational inequality
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Author(s):  
Soumia Saïdi

The main purpose of this work is to study the existence of solutions for a perturbed second-order evolution inclusion involving time-dependent subdifferential operators. Under suitable conditions on the set-valued perturbation, the main result of the paper is proved in the context of a separable Hilbert space. A second-order evolution quasi-variational inequality is also investigated.


Symmetry ◽  
2021 ◽  
Vol 13 (10) ◽  
pp. 1882
Author(s):  
Shih-Sen Chang ◽  
Salahuddin ◽  
Lin Wang ◽  
Gang Wang ◽  
Yunhe Zhao

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.


2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Hidekazu Yoshioka ◽  
Yuta Yaegashi

AbstractA stochastic impulse control problem with imperfect controllability of interventions is formulated with an emphasis on applications to ecological and environmental management problems. The imperfectness comes from uncertainties with respect to the magnitude of interventions. Our model is based on a dynamic programming formalism to impulsively control a 1-D diffusion process of a geometric Brownian type. The imperfectness leads to a non-local operator different from the many conventional ones, and evokes a slightly different optimal intervention policy. We give viscosity characterizations of the Hamilton–Jacobi–Bellman Quasi-Variational Inequality (HJBQVI) governing the value function focusing on its numerical computation. Uniqueness and verification results of the HJBQVI are presented and a candidate exact solution is constructed. The HJBQVI is solved with the two different numerical methods, an ordinary differential equation (ODE) based method and a finite difference scheme, demonstrating their consistency. Furthermore, the resulting controlled dynamics are extensively analyzed focusing on a bird population management case from a statistical standpoint.


2021 ◽  
Vol 26 (3) ◽  
pp. 444-468
Author(s):  
Othmane Baiz ◽  
Hicham Benaissa ◽  
Rachid Bouchantouf ◽  
Driss El Moutawakil

In the present paper, we analyze and study the control of a static thermoelastic contact problem. We consider a model which describes a frictional contact problem between a thermoelastic body and a deformable heat conductor obstacle. We derive a variational formulation of the model which is in the form of a coupled system of the quasi-variational inequality of elliptic type for the displacement and the nonlinear variational equation for the temperature. Then, under a smallness assumption, we prove the existence of a unique weak solution to the problem. Moreover, we establish the dependence of the solution with respect to the data and prove a convergence result. Finally, we introduce an optimization problem related to the contact model for which we prove the existence of a minimizer and provide a convergence result.


2021 ◽  
Vol 45 (4) ◽  
pp. 635-645
Author(s):  
MOHAMMED BEGGAS ◽  
◽  
MOHAMMED HAIOUR ◽  

In this paper, we present a maximum norm analysis of an overlapping Schwartz method on non matching grids for a quasi-variational inequality, where the obstacle and the second member depend on the solution. Our result improves and generalizes some previous results.


2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Shui-Lian Xie ◽  
Zhe Sun ◽  
Hong-Ru Xu

AbstractIn this paper, we consider the numerical method for solving finite-dimensional quasi-variational inequalities with both equality and inequality constraints. Firstly, we present a semismooth equation reformulation to the KKT system of a finite-dimensional quasi-variational inequality. Then we propose a semismooth Newton method to solve the equations and establish its global convergence. Finally, we report some numerical results to show the efficiency of the proposed method. Our method can obtain the solution to some problems that cannot be solved by the method proposed in (Facchinei et al. in Comput. Optim. Appl. 62:85–109, 2015). Besides, our method outperforms than the interior point method proposed in (Facchinei et al. in Math. Program. 144:369–412, 2014).


Mathematics ◽  
2021 ◽  
Vol 9 (14) ◽  
pp. 1658
Author(s):  
Shipra Singh ◽  
Aviv Gibali ◽  
Simeon Reich

We propose a multi-time generalized Nash equilibrium problem and prove its equivalence with a multi-time quasi-variational inequality problem. Then, we establish the existence of equilibria. Furthermore, we demonstrate that our multi-time generalized Nash equilibrium problem can be applied to solving traffic network problems, the aim of which is to minimize the traffic cost of each route and to solving a river basin pollution problem. Moreover, we also study the proposed multi-time generalized Nash equilibrium problem as a projected dynamical system and numerically illustrate our theoretical results.


Author(s):  
Irwin Yousept

This paper is devoted to the mathematical modeling and analysis of a hyperbolic Maxwell quasi-variational inequality (QVI) for  the Bean-Kim superconductivity model with temperature and magnetic field dependence in the critical current. Emerging from the Euler time discretization, we analyze the corresponding H(curl)-elliptic QVI and prove its existence using a fixed-point argument in combination with techniques from variational inequalities and Maxwell's equations.  Based on the existence result  for the H(curl)-elliptic QVI, we examine the  stability and convergence of the Euler scheme, which serve as our fundament for the well-posedness of the governing hyperbolic Maxwell QVI.


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