A modified Halpern algorithm for approximating a common solution of split equality convex minimization problem and fixed point problem in uniformly convex Banach spaces

Taiwo, Adeolu; Jolaoso, Lateef Olakunle

doi:10.1007/s40314-019-0841-5

Cited by 48 publications

(18 citation statements)

References 36 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…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

View full text Add to dashboard Cite

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.

show abstract

Section: Introductionmentioning

confidence: 99%

On Mixed Equilibrium Problems in Hadamard Spaces

Izuchukwu

Aremu

Oyewole

et al. 2019

Journal of Mathematics

View full text Add to dashboard Cite

show abstract

“…MPs are closely related to other optimization problems such as the monotone inclusion problems [21], equilibrium problems [23] (see also [19]), variational inequality problems [20] and many more. Thus, finding solutions of MPs using the PPA in Hilbert, Banach and Hadamard spaces still remains an active area of research in nonlinear and convex analysis and optimization see [1,2,8,15,16,31,38,39,40,43] and other references therein. In an attempt to introduced and generalized the PPA from these spaces to p-uniformly convex metric spaces, Choi and Ji [9] introduced the notion of p-resolvent operator in a p-uniformly convex metric space as a generalization of the Moreau-Yosida resolvent in a CAT(0) space as follows:…”

mentioning

confidence: 99%

Multi-step iterative algorithm for minimization and fixed point problems in p-uniformly convex metric spaces

Aremu¹,

Izuchukwu²,

Ogwo³

2021

JIMO

View full text Add to dashboard Cite

In this paper, we propose and study a multi-step iterative algorithm that comprises of a finite family of asymptotically k i -strictly pseudocontractive mappings with respect to p, and a p-resolvent operator associated with a proper convex and lower semicontinuous function in a p-uniformly convex metric space. Also, we establish the ∆-convergence of the proposed algorithm to a common fixed point of finite family of asymptotically k i -strictly pseudocontractive mappings which is also a minimizer of a proper convex and lower semicontinuous function. Furthermore, nontrivial numerical examples of our algorithm are given to show its applicability. Our results complement a host of recent results in literature.

show abstract

“…In recent years, SVIP has received great attention by many authors, who improved it in various ways, see, e.g. [22,35,37,43] and references therein, and it has been applied in different real-world problems such as intensity-modulated radiation therapy (IMRT), in sensor networks and in computerized tomography and data compression.…”

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

View full text Add to dashboard Cite

<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>

show abstract

A modified Halpern algorithm for approximating a common solution of split equality convex minimization problem and fixed point problem in uniformly convex Banach spaces

Cited by 48 publications

References 36 publications

On Mixed Equilibrium Problems in Hadamard Spaces

On Mixed Equilibrium Problems in Hadamard Spaces

Multi-step iterative algorithm for minimization and fixed point problems in p-uniformly convex metric spaces

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

Contact Info

Product

Resources

About