A Tseng extragradient method for solving variational inequality problems in Banach spaces

Oyewole, Olawale Kazeem; Abass, H. A.; Mebawondu, A. A.; Aremu, Kazeem Olalekan

doi:10.1007/s11075-021-01133-6

Cited by 11 publications

(8 citation statements)

References 30 publications

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“…To overcome this, authors have deviced several means which includes the use of an Armijo linesearch rule (a linesearch is a technique where the outside loop is determined by some inner calculation) (see Shehu and Iyiola 2019). Another means of avoiding the dependence of the method on the Lipschitz constant is by using a self adaptive method (see Oyewole et al 2021a and the references therein). Schematic approximation of a common solution of a system of variational inequality problems (CSVIP) has been considered in the literature.…”

Section: Introductionmentioning

confidence: 99%

Inertial self-adaptive Bregman projection method for finite family of variational inequality problems in reflexive Banach spaces

et al. 2022

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This paper considers an iterative approximation of a common solution of a finite family of variational inequailties in a real reflexive Banach space. By employing the Bregman distance and projection methods, we propose an iterative algorithm which uses a newly constructed adaptive step size to avoid a dependence on the Lipschitz constants of the families of the cost operators. The algorithm is carefully constructed so that the need to find a farthest element in any of its iterate is avoided. A strong convergence theorem was proved using the proposed method. We report some numerical experiments to illustrate the performance of the algorithm and also compare with existing methods in the literature.

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Section: Introductionmentioning

confidence: 99%

Inertial self-adaptive Bregman projection method for finite family of variational inequality problems in reflexive Banach spaces

et al. 2022

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“…Furthermore, iterative approximation of the various optimization problems is another interesting area of research in nonlinear analysis, especially in the twin concepts of fixed point and optimization theory. For extensive literature on the iterative methods for solving variational inequalities (see [16,17,20,22,25,29] and the reference therein). Also, for methods of approximating a solution of the EP in both the linear and nonlinear spaces, see [1,20,28,40].…”

Section: Introductionmentioning

confidence: 99%

On the existence and approximation of solutions of generalized equilibrium problem on Hadamard manifolds

et al. 2022

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In this paper, we study the existence of solution of the generalized equilibrium problem (GEP) in the framework of an Hadamard manifold. Using the KKM lemma, we prove the existence of solution of the GEP and give the properties of the resolvent function associated with the problem under consideration. Furthermore, we introduce an iterative algorithm for approximating a common solution of the GEP and a fixed point problem. Using the proposed method, we obtain and prove a strong convergence theorem for approximating a solution of the GEP, which is also a fixed point of a nonexpansive mapping under some mild conditions. We give an application of our convergence result to a solution of the convex minimization problem. To illustrate the convergence of the method, we report some numerical experiments. The result in this paper extends the study of the GEP from the linear settings to the Hadamard manifolds.

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“…For this reason, the Tseng extragradient method [16], initially introduced for solving variational inclusion problems, has been adopted for the solutions of VIPs. This method, which only uses one projection onto its feasible set, has been widely studied by authors; see, e.g., [17,18] and the references therein. Recently, Oyewole et al [17] introduced a totally relaxed, Tseng self-adaptive method for the solutions of VIPs in Banach spaces.…”

Section: Introductionmentioning

confidence: 99%

“…This method, which only uses one projection onto its feasible set, has been widely studied by authors; see, e.g., [17,18] and the references therein. Recently, Oyewole et al [17] introduced a totally relaxed, Tseng self-adaptive method for the solutions of VIPs in Banach spaces. They established a strong convergence theorem under some mild assumptions on the control parameters in the framework of 2-uniformly convex and uniformly smooth Banach spaces.…”

Section: Introductionmentioning

confidence: 99%

A totally relaxed self-adaptive algorithm for solving a variational inequality and fixed point problems in Banach spaces

2022

Appl. Set-Valued Anal. Optim.

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Using the Halpern iterative method, we propose and study a totally relaxed iterative algorithm for approximating a common solution to variational inequality and fixed point problems in certain Banach space. Our algorithm uses a self-adaptive step size to avoid the dependence on the Lipschitz constant of the operator involved. Our method can also find fixed points of Bregman firmly nonexpansive mappings. We establish a strong convergence theorem and present some numerical experiments to illustrate the performance of our algorithm.

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A Tseng extragradient method for solving variational inequality problems in Banach spaces

Cited by 11 publications

References 30 publications

Inertial self-adaptive Bregman projection method for finite family of variational inequality problems in reflexive Banach spaces

Inertial self-adaptive Bregman projection method for finite family of variational inequality problems in reflexive Banach spaces

On the existence and approximation of solutions of generalized equilibrium problem on Hadamard manifolds

A totally relaxed self-adaptive algorithm for solving a variational inequality and fixed point problems in Banach spaces

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