Hybrid Alternated Inertial Projection and Contraction Algorithm for Solving Bilevel Variational Inequality Problems by Jacob Ashiwere Abuchu, Austine Efut Ofem, Godwin Chidi Ugwunnadi, Ojen Kumar Narain, Azhar Hussain

“…This paper considers an alternated inertial-type extrapolation algorithm for solving bilevel pseudomonotone variational inequality problem in the framework of real Hilbert spaces with split variational inequality and fixed-point constraints of demimetric mapping. …”
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Strong Convergence of a Modified Extragradient Method to the Minimum-Norm Solution of Variational Inequalities by Yonghong Yao, Muhammad Aslam Noor, Yeong-Cheng Liou

“…We suggest and analyze a modified extragradient method for solving variational inequalities, which is convergent strongly to the minimum-norm solution of some variational inequality in an infinite-dimensional Hilbert space.…”
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The Conjugate Gradient Viscosity Approximation Algorithm for Split Generalized Equilibrium and Variational Inequality Problems by Meixia Li, Haitao Che, Jingjing Tan

“…In this paper, we study a kind of conjugate gradient viscosity approximation algorithm for finding a common solution of split generalized equilibrium problem and variational inequality problem. Under mild conditions, we prove that the sequence generated by the proposed iterative algorithm converges strongly to the common solution. …”
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A Note on the Regularity of the Solutions to Two Variational Inequalities Involving a Pseudodifferential Operator by Randolph G. Cooper

“…The regularity of solutions to variational inequalities involving local operators has been studied extensively. …”
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AN ITERATIVE ALGORITHM FOR GENERALISED MIXED EQUILIBRIUM PROBLEMS, VARIATIONAL INEQUALITY PROBLEMS AND OPTIMISATION PROBLEMS by Jong Soo Jung

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Subgradient Extragradient Method for Finite Lipschitzian Demicontractions and Variational Inequality Problems in a Hilbert Space by Sarawut Suwannaut

“…Then, a strong convergence theorem for finding a common element of the common fixed point set of finite Lipschitzian demicontraction mappings and the common solution set of variational inequality problems is established. Furthermore, numerical examples are given to support the main theorem.…”
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An Iteration to a Common Point of Solution of Variational Inequality and Fixed Point-Problems in Banach Spaces by H. Zegeye, N. Shahzad

“…We introduce an iterative process which converges strongly to a common point of solution of variational inequality problem for a monotone mapping and fixed point of uniformly Lipschitzian relatively asymptotically nonexpansive mapping in Banach spaces. …”
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A Generalized Strong Convergence Algorithm in the Presence of Errors for Variational Inequality Problems in Hilbert Spaces by Mostafa Ghadampour, Donal O’Regan, Ebrahim Soori, Ravi P. Agarwal

“…In this paper, we study the strong convergence of an algorithm to solve the variational inequality problem which extends a recent paper (Thong et al., Numerical Algorithms. 78, 1045-1060 (2018)). …”
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Self-Adaptive Predictor-Corrector Approach for General Variational Inequalities Using a Fixed-Point Formulation by Kubra Sanaullah, Saleem Ullah, Muhammad Shoaib Arif, Kamaleldin Abodayeh, Rabia Fayyaz

“…A literature review revealed that the general variational inequalities, fixed-point problems, and Winner–Hopf equations are equivalent. …”
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Viscosity Approximation Methods for Equilibrium Problems, Variational Inequality Problems of Infinitely Strict Pseudocontractions in Hilbert Spaces by Aihong Wang

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A Hybrid Method for a Countable Family of Multivalued Maps, Equilibrium Problems, and Variational Inequality Problems by Watcharaporn Cholamjiak, Suthep Suantai

“…We introduce a new monotone hybrid iterative scheme for finding a common element of the set of common fixed points of a countable family of nonexpansive multivalued maps, the set of solutions of variational inequality problem, and the set of the solutions of the equilibrium problem in a Hilbert space. …”
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Convergence Theorem for Equilibrium and Variational Inequality Problems and a Family of Infinitely Nonexpansive Mappings in Hilbert Space by Zhou Yinying, Cao Jiantao, Wang Yali

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Algorithm for Solutions of Nonlinear Equations of Strongly Monotone Type and Applications to Convex Minimization and Variational Inequality Problems by Mathew O. Aibinu, Surendra C. Thakur, Sibusiso Moyo

“…As a consequence of the main result, the solutions of convex minimization and variational inequality problems are obtained. This solution has applications in other fields such as engineering, physics, biology, chemistry, economics, and game theory.…”
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Yosida Complementarity Problem with Yosida Variational Inequality Problem and Yosida Proximal Operator Equation Involving XOR-Operation by Rais Ahmad, Arvind Kumar Rajpoot, Imran Ali, Ching-Feng Wen

“…Due to the importance of Yosida approximation operator, we generalized the variational inequality problem and its equivalent problems by using Yosida approximation operator. …”
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Relaxed Extragradient Methods with Regularization for General System of Variational Inequalities with Constraints of Split Feasibility and Fixed Point Problems by L. C. Ceng, A. Petruşel, J. C. Yao

“…We suggest and analyze relaxed extragradient iterative algorithms with regularization for finding a common element of the solution set of a general system of variational inequalities, the solution set of a split feasibility problem, and the fixed point set of a strictly pseudocontractive mapping defined on a real Hilbert space. …”
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A Hybrid Extragradient-Like Method for Variational Inequalities, Equilibrium Problems, and an Infinitely Family of Strictly Pseudocontractive Mappings by Yaqin Wang, Hongkun Xu, Xiaoli Fang

“…The purpose of this paper is to consider a new scheme by the hybrid extragradient-like method for finding a common element of the set of solutions of a generalized mixed equilibrium problem, the set of solutions of a variational inequality, and the set of fixed points of an infinitely family of strictly pseudocontractive mappings in Hilbert spaces. …”
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Hybrid Extragradient Method with Regularization for Convex Minimization, Generalized Mixed Equilibrium, Variational Inequality and Fixed Point Problems by Lu-Chuan Ceng, Juei-Ling Ho

“…We introduce two iterative algorithms by the hybrid extragradient method with regularization for finding a common element of the set of solutions of the minimization problem for a convex and continuously Fréchet differentiable functional, the set of solutions of finite generalized mixed equilibrium problems, the set of solutions of finite variational inequalities for inverse strong monotone mappings and the set of fixed points of an asymptotically κ-strict pseudocontractive mapping in the intermediate sense in a real Hilbert space. …”
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A temperature control problem by Ioannis Athanasopoulos

Subjects: “…variational inequalities…”
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An Iterative Method for Solving Split Monotone Variational Inclusion Problems and Finite Family of Variational Inequality Problems in Hilbert Spaces by Wanna Sriprad, Somnuk Srisawat

“…The purpose of this paper is to study the convergence analysis of an intermixed algorithm for finding the common element of the set of solutions of split monotone variational inclusion problem (SMIV) and the set of a finite family of variational inequality problems. Under the suitable assumption, a strong convergence theorem has been proved in the framework of a real Hilbert space. …”
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The Mann-Type Extragradient Iterative Algorithms with Regularization for Solving Variational Inequality Problems, Split Feasibility, and Fixed Point Problems by Lu-Chuan Ceng, Himanshu Gupta, Ching-Feng Wen

“…The purpose of this paper is to introduce and analyze the Mann-type extragradient iterative algorithms with regularization for finding a common element of the solution set Ξ of a general system of variational inequalities, the solution set Γ of a split feasibility problem, and the fixed point set Fix(S) of a strictly pseudocontractive mapping S in the setting of the Hilbert spaces. …”
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