An iterative algorithm for solving variational inequality, generalized mixed equilibrium, convex minimization and zeros problems for a class of nonexpansive-type mappings

Alakoya, Timilehin Opeyemi; Taiwo, Adeolu; Mewomo, Oluwatosin Temitope; Cho, Yeol Je

doi:10.1007/s11565-020-00354-2

Cited by 44 publications

(21 citation statements)

References 52 publications

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“…Recently, several authors have studied and proposed many iterative algorithms for approximating the solutions of variational inequality problem and related optimization problems (see [25,28,29]). The generalized mixed equilibrium problem is very general in the sense that it includes as a special case minimization problems, variational inequality problems, fixed point problems, Nash equilibrium problems in noncooperative games, and many others (see [2,3,7,12,16,18,21,26,[48][49][50]52]).…”

Section: Introductionmentioning

confidence: 99%

Krasnoselski–Mann-type inertial method for solving split generalized mixed equilibrium and hierarchical fixed point problems

Chuasuk

Kaewcharoen

2021

J Inequal Appl

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In this paper, we present Krasnoselski–Mann-type inertial method for solving split generalized mixed equilibrium and hierarchical fixed point problems for k-strictly pseudocontractive nonself-mappings. We establish that the weak convergence of the proposed accelerated iterative method with inertial terms involves a step size which does not require any prior knowledge of the operator norm under several suitable conditions in Hilbert spaces. Finally, the application to a Nash–Cournot oligopolistic market equilibrium model is discussed, and numerical examples are provided to demonstrate the effectiveness of our iterative method.

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Section: Introductionmentioning

confidence: 99%

Krasnoselski–Mann-type inertial method for solving split generalized mixed equilibrium and hierarchical fixed point problems

Chuasuk

Kaewcharoen

2021

J Inequal Appl

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“…where F : C × C → R is a bifunction. The EP unify many important problems, such as variational inequalities, fixed point problems, optimization problems, saddle point (minmax) problems, Nash equilibria problems and complimentarity problems [2][3][4][5][6][7]. It also finds applications in other fields of studies like physics, economics, engineering and so on [1,2,[8][9][10].…”

Section: Introductionmentioning

confidence: 99%

“…The SFP has been studied by researchers due to its applications in various field of science and technology, such as signal processing, intensity-modulated radiation therapy and medical image construction, for details, see [39,40]. In solving (5), Byrne [39] introduced the following iterative algorithm: let x 0 ∈ R n be arbitrary,…”

Section: Introductionmentioning

confidence: 99%

A Strong Convergence Theorem for Split Null Point Problem and Generalized Mixed Equilibrium Problem in Real Hilbert Spaces

Oyewole

2021

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In this paper, we study a schematic approximation of solutions of a split null point problem for a finite family of maximal monotone operators in real Hilbert spaces. We propose an iterative algorithm that does not depend on the operator norm which solves the split null point problem and also solves a generalized mixed equilibrium problem. We prove a strong convergence of the proposed algorithm to a common solution of the two problems. We display some numerical examples to illustrate our method. Our result improves some existing results in the literature.

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“…In the early 1960's, Stampacchia [43] and Fichera [12] introduced the theory of variational inequality problem. The Problem (1) is a fundamental problem which has a wide range of applications in applied field of mathematics such as network equilibrium problems, complementary problems, optimization theory and systems of nonlinear equations (see [5,13,19,24,27,28,40,48]). Under suitable conditions, there are generally two main approaches to finding the solutions of VIP (1).…”

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confidence: 99%

A new inertial-projection algorithm for approximating common solution of variational inequality and fixed point problems of multivalued mappings

Owolabi¹,

Alakoya²,

Taiwo³

et al. 2022

NACO

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In this paper, we present a new modified self-adaptive inertial subgradient extragradient algorithm in which the two projections are made onto some half spaces. Moreover, under mild conditions, we obtain a strong convergence of the sequence generated by our proposed algorithm for approximating a common solution of variational inequality problem and common fixed point of a finite family of demicontractive mappings in a real Hilbert space. The main advantages of our algorithm are: strong convergence result obtained without prior knowledge of the Lipschitz constant of the related monotone operator, the two projections made onto some half-spaces and the inertial technique which speeds up rate of convergence. Finally, we present an application and a numerical example to illustrate the usefulness and applicability of our algorithm.

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An iterative algorithm for solving variational inequality, generalized mixed equilibrium, convex minimization and zeros problems for a class of nonexpansive-type mappings

Cited by 44 publications

References 52 publications

Krasnoselski–Mann-type inertial method for solving split generalized mixed equilibrium and hierarchical fixed point problems

Krasnoselski–Mann-type inertial method for solving split generalized mixed equilibrium and hierarchical fixed point problems

A Strong Convergence Theorem for Split Null Point Problem and Generalized Mixed Equilibrium Problem in Real Hilbert Spaces

A new inertial-projection algorithm for approximating common solution of variational inequality and fixed point problems of multivalued mappings

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