A Trial-and-Error Method with Autonomous Vehicle-to-Infrastructure Traffic Counts for Cordon-Based Congestion Pricing by Zhiyuan Liu, Yong Zhang, Shuaian Wang, Zhibin Li

“…Then, the stochastic user equilibrium (SUE) with asymmetric link travel time functions is used to assess each feasible toll pattern. Based on a variational inequality (VI) model for the optimal toll pattern, this study proposes a theoretically convergent trial-and-error method for the addressed problem, where only traffic counts data are needed. …”
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Decision Optimization of Low-Carbon Dual-Channel Supply Chain of Auto Parts Based on Smart City Architecture by Zheng Liu, Bin Hu, Bangtong Huang, Lingling Lang, Hangxin Guo, Yuanjun Zhao

“…This paper analyzes the optimal decision-making behavior and interaction of suppliers, producers, physical retailers, online retailers, demand markets, and recyclers in the auto parts industry, constructs the economic and environmental objective functions of low-carbon supply chain management, applies variational inequality to analyze the optimal conditions of the whole low-carbon supply chain system, and finally carries out simulation calculation. …”
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Two General Algorithms for Computing Fixed Points of Nonexpansive Mappings in Banach Spaces by Shuang Wang

“…Moreover, the fixed points solve the same system of nonlinear variational inequalities.…”
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A New System of Generalized Mixed Quasivariational Inclusions with Relaxed Cocoercive Operators and Applications by Zhongping Wan, Jia-Wei Chen, Hai Sun, Liuyang Yuan

“…A new system of generalized mixed quasivariational inclusions (for short, SGMQVI) with relaxed cocoercive operators, which develop some preexisting variational inequalities, is introduced and investigated in Banach spaces. …”
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On Abstract Economies and Their Applications by Chien-Hao Huang, Liang-Ju Chu

“…As an application, we derive an existence theorem of generalized quasi-variational inequalities in the general setting of -spaces without any linear structure.…”
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On Mann’s Type Method for Nonexpansive and Strongly Quasinonexpansive Mappings in Hilbert Spaces by Nawab Hussain, Giuseppe Marino, Badriah A. S. Alamri

“…In the setting of Hilbert spaces, we study Mann’s type method to approximate strong solutions of variational inequalities. We show that these solutions are fixed points of a nonexpansive mapping and/or a strongly quasinonexpansive mapping, depending on the coefficients involved in the algorithm.…”
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L∞-error estimate for a system of elliptic quasivariational inequalities by M. Boulbrachene, M. Haiour, S. Saadi

“…Under W2,p(Ω)-regularity of the continuous solution, a quasi-optimal L∞-convergence of a piecewise linear finite element method is established, involving a monotone algorithm of Bensoussan-Lions type and standard uniform error estimates known for elliptic variational inequalities (VIs).…”
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Three-step iterations for mixed quasi variational-like inequalities by Muhammad Aslam Noor

“…As special cases, we obtain various new and known methods for solving variational inequalities and related optimization problems.…”
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Nonpivot and Implicit Projected Dynamical Systems on Hilbert Spaces by Monica Gabriela Cojocaru, Stephane Pia

“…The generalization consists of showing the existence of such systems and their relation to variational problems, such as variational inequalities. In the case of usual Hilbert spaces these systems have been extensively studied, and, as in previous works, this new generalization has been motivated by applications, as shown below.…”
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Finite Difference Method for Solving a System of Third-Order Boundary Value Problems by Muhammad Aslam Noor, Eisa Al-Said, Khalida Inayat Noor

“…Schwartz (1990)), and can be studied in the framework of variational inequalities. We show that the present method is of order three and give numerical results that are better than the other available results. …”
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On Flows of Bingham-Type Fluids with Threshold Slippage by Evgenii S. Baranovskii

“…We investigate a mathematical model describing 3D steady-state flows of Bingham-type fluids in a bounded domain under threshold-slip boundary conditions, which state that flows can slip over solid surfaces when the shear stresses reach a certain critical value. Using a variational inequalities approach, we suggest the weak formulation to this problem. …”
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Mathematical Formulation of Soft-Contact Problems for Various Rheological Models of Damper by Wiesław Grzesikiewicz, Artur Zbiciak

“…The mathematical descriptions of soft-contact problems involving variational inequalities are presented. The main finding of the paper is a method of description of soft-contact phenomenon between rigid object and deformable rheological structure by the system of explicit nonlinear differential-algebraic equations easy for numerical implementation. …”
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Classical and Impulse Stochastic Control on the Optimization of Dividends with Residual Capital at Bankruptcy by Peimin Chen, Bo Li

“…In order to solve this problem, we reduce it to quasi-variational inequalities with a nonzero boundary condition. …”
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Analysis of electroelastic frictionless contact problems with adhesion by Mircea Sofonea, Rachid Arhab, Raafat Tarraf

“…The proofs are based on arguments of time-dependent variational inequalities, differential equations, and fixed point. …”
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Mixed quasi invex equilibrium problems by Muhammad Aslam Noor

“…This class of invex equilibrium problems includes equilibrium problems, variational inequalities, and variational-like inequalities as special cases. …”
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Calculus Rules for V-Proximal Subdifferentials in Smooth Banach Spaces by Messaoud Bounkhel

“…Applications to nonconvex minimisation problems and nonconvex variational inequalities are established.…”
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On the existence of solutions of the system of nonlinear quasi-mixed equilibrium problems and their stability of the procedure scheme by Satit Saejung

“…Finally, we examine and improve the convergence theorem for solving a system of variational inequalities as established by Chang et al. (Appl. …”
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Pricing of American Carbon Emission Derivatives and Numerical Method under the Mixed Fractional Brownian Motion by Yuling Wang, Jing Wang

“…We have outlined a power penalty approach using parabolic variation inequality and linear complementarity (LCP) which arises from mixed fractional Brownian motion. …”
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Viscosity Approximation Methods for Nonexpansive Nonself-Mappings in Hilbert Spaces by Rabian Wangkeeree

“…Strong convergence of the sequences {xn},{yn}, and {zn} to a fixed point of T which solves some variational inequalities is obtained under certain appropriate conditions on the real sequences {αn} and {tn}.…”
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