Modified inertial subgradient extragradient method with self adaptive stepsize for solving monotone variational inequality and fixed point problems

Alakoya, Timilehin Opeyemi; Jolaoso, Lateef Olakunle; Mewomo, Oluwatosin Temitope

doi:10.1080/02331934.2020.1723586

Cited by 70 publications

(43 citation statements)

References 44 publications

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“…The inertial method involves a two-step iteration in which the next iterate is defined by making use of the previous two iterates and this generally increase the rate of convergence of iterative algorithms. The inertial type algorithm has been studied and modified in various forms by many authors (see [2,3,4,9,47,51,52]). For example, an inertial hybrid proximal-extragradient algorithm which is a combination of hybrid proximal extragradient and inertial type algorithm for a maximal monotone operator was proposed by Bot and Csetnek [9].…”

Section:     mentioning

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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Section:     mentioning

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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“…Lemma 2.5. [43] Let { } a n be a sequence of nonnegative real numbers, { } α n be a sequence in is a continuous and monotone mapping, then * x is a solution of (1) if and only if *…”

Section: Preliminariesmentioning

confidence: 99%

Two modifications of the inertial Tseng extragradient method with self-adaptive step size for solving monotone variational inequality problems

Alakoya

Jolaoso

2020

Demonstratio Mathematica

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In this work, we introduce two new inertial-type algorithms for solving variational inequality problems (VIPs) with monotone and Lipschitz continuous mappings in real Hilbert spaces. The first algorithm requires the computation of only one projection onto the feasible set per iteration while the second algorithm needs the computation of only one projection onto a half-space, and prior knowledge of the Lipschitz constant of the monotone mapping is not required in proving the strong convergence theorems for the two algorithms. Under some mild assumptions, we prove strong convergence results for the proposed algorithms to a solution of a VIP. Finally, we provide some numerical experiments to illustrate the efficiency and advantages of the proposed algorithms.

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“…We denote by F (S), the set of all fixed points of S. Iterative methods for finding fixed point of nonlinear mappings have recently been applied to solve convex minimization and related optimization problems, see e.g. [3,18,20,21,23,34,36,42,45,49,50] and the references therein. Convex minimization problems have greatly influenced the development of nearly all branches of pure and applied sciences.…”

Section: Introduction In 2011 Moudafimentioning

confidence: 99%

A self adaptive inertial algorithm for solving split variational inclusion and fixed point problems with applications

Alakoya¹,

Jolaoso²

2022

JIMO

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<p style='text-indent:20px;'>We propose a general iterative scheme with inertial term and self-adaptive stepsize for approximating a common solution of Split Variational Inclusion Problem (SVIP) and Fixed Point Problem (FPP) for a quasi-nonexpansive mapping in real Hilbert spaces. We prove that our iterative scheme converges strongly to a common solution of SVIP and FPP for a quasi-nonexpansive mapping, which is also a solution of a certain optimization problem related to a strongly positive bounded linear operator. We apply our proposed algorithm to the problem of finding an equilibrium point with minimal cost of production for a model in industrial electricity production. Numerical results are presented to demonstrate the efficiency of our algorithm in comparison with some other existing algorithms in the literature.</p>

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Modified inertial subgradient extragradient method with self adaptive stepsize for solving monotone variational inequality and fixed point problems

Cited by 70 publications

References 44 publications

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

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

Two modifications of the inertial Tseng extragradient method with self-adaptive step size for solving monotone variational inequality problems

A self adaptive inertial algorithm for solving split variational inclusion and fixed point problems with applications

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