Inertial Scheme for Solving Two-Level Variational Inequality and Fixed Point Problem Involving Pseudomonotone and ϱ — Demimetric Mappings

Godwin, Emeka C.; Araka, N. N.; Okeke, Godwin Amechi; Ezeamama, Grace C.

doi:10.21203/rs.3.rs-1774494/v1

Cited by 6 publications

(6 citation statements)

References 33 publications

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“…It is worthy of note that variational inequality problems, convex feasibility problems, monotone inclusion problems, convex optimization problems, and image restoration problems can all be formulated as finding the fixed points of suitable nonlinear mappings; see [7,11]. Several methods have been proposed for approximating fixed points of nonlinear mappings (see [20,32,[38][39][40][41]51]) and the reference therein.…”

Section: Introductionmentioning

confidence: 99%

An inertial viscosity algorithm for solving monotone variational inclusion and common fixed point problems of strict pseudocontractions

Alakoya

Ogunsola

2023

Bol. Soc. Mat. Mex.

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In this paper, we study the problem of finding the solution of monotone variational inclusion problem (MVIP) with constraint of common fixed point problem (CFPP) of strict pseudocontractions. We propose a new viscosity method, which combines the inertial technique with self-adaptive step size strategy for approximating the solution of the problem in the framework of Hilbert spaces. Unlike several of the existing results in the literature, our proposed method does not require the co-coerciveness and Lipschitz continuity assumptions of the associated single-valued operator. Also, our method does not involve any linesearch technique which could be time-consuming, rather we employ a self-adaptive step size technique that generates a nonmonotonic sequence of step sizes. Moreover, we prove strong convergence result for our algorithm under some mild conditions and apply our result to study other optimization problems. We present several numerical experiments to demonstrate the computational advantage of our proposed method over the existing methods in the literature. Our result complements several of the existing results in the current literature in this direction.

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Section: Introductionmentioning

confidence: 99%

An inertial viscosity algorithm for solving monotone variational inclusion and common fixed point problems of strict pseudocontractions

Alakoya

Ogunsola

2023

Bol. Soc. Mat. Mex.

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“…Also, problem () is more general than the Split Monotone Variational Inclusion Problem (SMVIP) introduced and studied by Moudafi 17 . Thus, problem () includes inherently many other vital problems including split saddle point problems, split minimization problems, split equilibrium problems, monotone inclusion problems, among others (see, e.g., previous works 17–28 ). Another motivation for studying problem () lies in its potential application to mathematical models whose constraints can be expressed as ().…”

Section: Introductionmentioning

confidence: 99%

“…includes inherently many other vital problems including split saddle point problems, split minimization problems, split equilibrium problems, monotone inclusion problems, among others (see, e.g., previous works [17][18][19][20][21][22][23][24][25][26][27][28] ). Another motivation for studying problem (1.7) lies in its potential application to mathematical models whose constraints can be expressed as (1.7).…”

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confidence: 99%

Image restorations using a modified relaxed inertial technique for generalized split feasibility problems

Godwin

Izuchukwu

2022

Math Methods in App Sciences

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In this article, we propose a new efficient self‐adaptive method and prove that it converges strongly to a minimum‐norm solution of a generalized split feasibility problem in real Hilbert spaces. The proposed method is derived from a definite discrete dynamical system in time, which combines both the relaxation and inertial techniques for the purpose of increasing the rate of convergence of the iterative scheme. Furthermore, the method requires the monotonicity and Lipschitz continuity condition of the underlying single‐valued cost operator A$$ A $$, and it employs some simple self‐adaptive stepsizes that are generated at each iteration by some easy computations. As a by‐product, we obtain methods for solving other classes of generalized split feasibility problems in real Hilbert spaces. Two major merits of our scheme in solving image restoration problems over related schemes are the higher signal‐to‐noise ratio value and lower CPU time for generating recovered images. Finally, we analyze our methods with different related strong convergent methods in the literature.

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“…It is known that many problems in economics can be reduce to problem (1.1). Since the introduction of EP (1.1) by Blum and Oettli [4], many authors have used various iterative algorithms, such as Halpern, viscosity, hybrid, cyclic, shrinking, and so on to approximate solutions of EP (1.1) in Hilbert and Banach space; see, e.g., [5,6,7,8,9,10,11,12,13] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

On split equality generalized equilibrium problems and fixed point problems of Bregman relatively nonexpansive semigroups

2022

J. Appl. Numer. Optim.

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In this paper, we introduce a new split inverse problem called the split equality generalized equilibrium problem which is more general than the split feasibility problem, the split equilibrium problem, and the split equality equilibrium problem. We develop an iterative algorithm for approximating a common solution of this problem and the split equality fixed point problem for Bregman relatively nonexpansive semigroups in p-uniformly convex and uniformly smooth Banach spaces. Using our iterative algorithm, we prove a strong convergence theorem and investigate a split equality convex optimization problem as an application. Finally, we present some numerical experiments to demonstrate the applicability of our proposed method.

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Inertial Scheme for Solving Two-Level Variational Inequality and Fixed Point Problem Involving Pseudomonotone and ϱ — Demimetric Mappings

Cited by 6 publications

References 33 publications

An inertial viscosity algorithm for solving monotone variational inclusion and common fixed point problems of strict pseudocontractions

An inertial viscosity algorithm for solving monotone variational inclusion and common fixed point problems of strict pseudocontractions

Image restorations using a modified relaxed inertial technique for generalized split feasibility problems

On split equality generalized equilibrium problems and fixed point problems of Bregman relatively nonexpansive semigroups

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