A viscosity iterative algorithm for a family of monotone inclusion problems in an Hadamard space

Ogwo, G. N.; Izuchukwu, Chinedu; Aremu, Kazeem Olalekan

doi:10.36045/bbms/1590199308

Cited by 31 publications

(15 citation statements)

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“…In this case, x * is called a minimizer of Ψ and argmin y∈C Ψ(y) denotes the set of minimizers of Ψ. MPs are very useful in optimization theory and convex and nonlinear analysis. One of the most popular and effective methods for solving MPs is the proximal point algorithm (PPA) which was introduced in Hilbert space by Martinet [1] in 1970 and was further extensively studied in the same space by Rockafellar [2] in 1976. e PPA and its generalizations have also been studied extensively for solving MP (1) and related optimization problems in Banach spaces and Hadamard manifolds (see [3][4][5][6][7] and the references therein), as well as in Hadamard and p-uniformly convex metric spaces (see [8][9][10][11][12][13] and the references therein).…”

Section: Introductionmentioning

confidence: 99%

On Mixed Equilibrium Problems in Hadamard Spaces

Izuchukwu

Aremu

Oyewole

et al. 2019

Journal of Mathematics

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The main purpose of this paper is to study mixed equilibrium problems in Hadamard spaces. First, we establish the existence of solution of the mixed equilibrium problem and the unique existence of the resolvent operator for the problem. We then prove a strong convergence of the resolvent and a Δ-convergence of the proximal point algorithm to a solution of the mixed equilibrium problem under some suitable conditions. Furthermore, we study the asymptotic behavior of the sequence generated by a Halpern-type PPA. Finally, we give a numerical example in a nonlinear space setting to illustrate the applicability of our results. Our results extend and unify some related results in the literature.

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Section: Introductionmentioning

confidence: 99%

On Mixed Equilibrium Problems in Hadamard Spaces

Izuchukwu

Aremu

Oyewole

et al. 2019

Journal of Mathematics

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“…MPs play vital role in nonlinear analysis and geometry. They have notable applications in computer vision, machine learning, electronic structure computation, system balancing and robot manipulation, and several iterative algorithms have been studied for solving MPs and related optimization problems (see [1,4,5,19,20,22,23,24,25,26,34,33,36,42,43,44,48] and references therein). The Proximal Point Algorithm (PPA) is one of the most popular and effective methods for solving MPs.…”

Section: Minimization and Fixed Point Problems For Non-self Mappings 307mentioning

confidence: 99%

A convergence theorem for approximating minimization and fixed point problems for non-self mappings in Hadamard spaces

Aremu¹,

Izuchukwu²,

Oyewole³

2021

Revista De La Unión Matemática Argentina

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We propose a modified Halpern-type algorithm involving a Lipschitz hemicontractive non-self mapping and the resolvent of a convex function in a Hadamard space. We obtain a strong convergence of the proposed algorithm to a minimizer of a convex function which is also a fixed point of a Lipschitz hemicontractive non-self mapping. Furthermore, we give a numerical example to illustrate and support our method. Our proposed method improves and extends some recent works in the literature.

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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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A viscosity iterative algorithm for a family of monotone inclusion problems in an Hadamard space

Cited by 31 publications

References 0 publications

On Mixed Equilibrium Problems in Hadamard Spaces

On Mixed Equilibrium Problems in Hadamard Spaces

A convergence theorem for approximating minimization and fixed point problems for non-self mappings in Hadamard spaces

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

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