Iterative approaches to solving convex minimization problems and fixed point problems in complete CAT(0) spaces

Lerkchaiyaphum, Kritsada; Phuengrattana, Withun

doi:10.1007/s11075-017-0337-6

Cited by 5 publications

(2 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The problem of finding minimizers of convex functions which are also fixed points of nonlinear mappings has recently been studied in the framework of Hadamard spaces (see [3,9,21,29,40] and references therein). However, the mappings used are mostly self mappings.…”

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

View full text Add to dashboard Cite

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.

show abstract

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

View full text Add to dashboard Cite

show abstract

“…Also, they established the Δ-convergence for sequence fs n g generated by (9). Motivated by the results of Liu and Chang [17], the authors in [21] introduced a modified PPA for finding a common solution of convex minimization problems and fixed point of nonexpansive mappings in CAT(0) spaces. In particular, the authors proved the Δ -convergence for the following results.…”

Section: Introductionmentioning

confidence: 99%

Strong Convergence Theorem for Finding a Common Solution of Convex Minimization and Fixed Point Problems in CAT(0) Spaces

Ndlovu

Jolaoso

Aphane

2022

Abstract and Applied Analysis

View full text Add to dashboard Cite

In this paper, we introduce a proximal point algorithm for approximating a common solution of finite family of convex minimization problems and fixed point problems fork-demicontractive mappings in complete CAT(0) spaces. We prove a strong convergence result and obtain other consequence results which generalize and extend some recent results in the literature. We further provide a numerical example to illustrate the convergence behaviour of the sequence generated by our algorithm.

show abstract

First Order Methods for Optimization on Riemannian Manifolds

Ferreira

Louzeiro

Prudente

2020

Handbook of Variational Methods for Nonlinear Geometric Data

View full text Add to dashboard Cite

Iterative approaches to solving convex minimization problems and fixed point problems in complete CAT(0) spaces

Cited by 5 publications

References 14 publications

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

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

Strong Convergence Theorem for Finding a Common Solution of Convex Minimization and Fixed Point Problems in CAT(0) Spaces

First Order Methods for Optimization on Riemannian Manifolds

Contact Info

Product

Resources

About