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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A Heuristic Algorithm for Constrained Multi-Source Location Problem with Closest Distance under Gauge: The Variational Inequality Approach by Jian-Lin Jiang, Saeed Assani, Kun Cheng, Xiao-Xing Zhu

“…In the location phase, the single-source subproblem with regional demands is reformulated into an equivalent linear variational inequality (LVI), and then, a projection-contraction (PC) method is adopted to find the optimal locations of facilities, whereas in the allocation phase, the regional customers are allocated to facilities according to the nearest center reclassification (NCR). …”
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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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Sobolev estimates and inverse Hölder estimates on a class of non-divergence variation-inequality problem arising in American option pricing by Kaiyu Zhang

Subjects: “…variation-inequality problems…”
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An Inertial Iterative Algorithm to Find Common Solution of a Split Generalized Equilibrium and a Variational Inequality Problem in Hilbert Spaces by Mohammad Farid, Rehan Ali, Watcharaporn Cholamjiak

“…In this paper, we introduce and study an iterative algorithm via inertial and viscosity techniques to find a common solution of a split generalized equilibrium and a variational inequality problem in Hilbert spaces. Further, we prove that the sequence generated by the proposed theorem converges strongly to the common solution of our problem. …”
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A New Iterative Scheme for Generalized Mixed Equilibrium, Variational Inequality Problems, and a Zero Point of Maximal Monotone Operators by Kriengsak Wattanawitoon, Poom Kumam

“…The purpose of this paper is to introduce a new iterative scheme for finding a common element of the set of solutions of generalized mixed equilibrium problems, the set of solutions of variational inequality problems, the zero point of maximal monotone operators, and the set of two countable families of quasi-ϕ-nonexpansive mappings in Banach spaces. …”
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LOWER SEMI-CONTINUITY OF THE SOLUTION SET TO A PARAMETRIC OPTIMAL CONTROL PROBLEM by Bùi Trọng Kiên, Nguyễn Thị Toàn, Mu Ming Wong, Jen Chih Yao

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Strong Convergence of a Hybrid Projection Algorithm for Equilibrium Problems, Variational Inequality Problems and Fixed Point Problems in a Banach Space by Wariam Chuayjan, Sornsak Thianwan

“…We introduce and study a new hybrid projection algorithm for finding a common element of the set of solutions of an equilibrium problem, the set of common fixed points of relatively quasi-nonexpansive mappings, and the set of solutions of the variational inequality for an inverse-strongly-monotone operator in a Banach space. …”
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Viscosity Approximation Methods with Errors and Strong Convergence Theorems for a Common Point of Pseudocontractive and Monotone Mappings: Solutions of Variational Inequality Problems by Yan Tang

“…We introduce two proximal iterative algorithms with errors which converge strongly to the common solution of certain variational inequality problems for a finite family of pseudocontractive mappings and a finite family of monotone mappings. …”
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The $ {L^\infty } $ estimate of the spatial gradient of the solution to a variational inequality problem originates from the financial contract problem with advanced implementation clauses by Qingjun Zhao

Subjects: “…variational inequality problem…”
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Variational Analysis of a Dynamic Contact Problem with Wear and Damage Involving Viscoelastic Materials with Long-Term Memory by Ahmed Hamidat, Hakim Bagua, Adel Aissaoui

Subjects: “…Hyperbolic. Quasi-variational inequality.…”
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A frictional contact problem with normal damped response conditions and thermal effects for a thermo-electro-viscoelastic material by Abdelmoumene Djabi

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Hybrid Iterative Scheme by a Relaxed Extragradient Method for Equilibrium Problems, a General System of Variational Inequalities and Fixed-Point Problems of a Countable Family of Nonexpansive Mappings by Qiao-Li Dong, Yan-Ni Guo, Fang Su

“…Based on the relaxed extragradient method and viscosity method, we introduce a new iterative method for finding a common element of solution of equilibrium problems, the solution set of a general system of variational inequalities, and the set of fixed points of a countable family of nonexpansive mappings in a real Hilbert space. …”
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CONTROL PROBLEMS FOR NONLINEAR VARIATIONAL EVOLUTION INEQUALITIES by Su Jin Cheon

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THE TIKHONOV REGULARISATION METHOD FOR PSEUDOMONOTONE EQUILIBRIUM PROBLEMS by Phạm Gia Hưng, Lê Dũng Mưu

Subjects: “…Multi-valued variational inequalities…”
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Regularization method and a posteriori error estimates for the two membranes problem by Bouchlaghem Mohammed, Mermri El Bekkaye, Mellah Zhor

Subjects: “…variational inequalities…”
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Dynamic Traffic Network Model and Time-Dependent Braess’ Paradox by Chunxue Zhao

“…We propose a dynamic traffic network model and give the equilibrium condition and the equivalent variational inequality of the network. In this model, instead of the influence of inflow rate and output rate on the link congestion, the influence of the adjacent links at the same paths is considered; in this case, the equivalence between the equilibrium condition and the variational inequality is proved. …”
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