Proximal point algorithms for solving convex minimization problem and common fixed points problem of asymptotically quasi-nonexpansive mappings in CAT(0) spaces with convergence analysis

DOI10.1007/s11075-017-0402-1zbMath1398.65112OpenAlexW2745945010WikidataQ59306801 ScholiaQ59306801MaRDI QIDQ1652795

Poom Kumam, Nuttapol Pakkaranang, Yeol Je Cho

Publication date: 16 July 2018

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11075-017-0402-1

zbMATH Keywords

CAT(0) spacescommon fixed pointproximal point algorithmconvex minimization problemasymptotically quasi-nonexpansive mapping

Mathematics Subject Classification ID

Fixed-point and coincidence theorems (topological aspects) (54H25) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09) Numerical solutions to equations with nonlinear operators (65J15)

Related Items (19)

\( \Delta \)-convergence for proximal point algorithm and fixed point problem in CAT(0) spaces ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Modified proximal point algorithms involving convex combination technique for solving minimization problems with convergence analysis ⋮ First Order Methods for Optimization on Riemannian Manifolds ⋮ Remarks on the approximate fixed point sequence of \((\alpha ,\beta)\)-maps ⋮ Unnamed Item ⋮ A modified proximal point algorithm for a nearly asymptotically quasi-nonexpansive mapping with an application ⋮ Unnamed Item ⋮ Modified viscosity type iteration for total asymptotically nonexpansive mappings in CAT(0) spaces and its application to optimization problems ⋮ Mann iteration for monotone nonexpansive mappings in ordered CAT(0) space with an application to integral equations ⋮ A modified proximal point algorithm involving nearly asymptotically quasi-nonexpansive mappings ⋮ A multi-step approximant for fixed point problem and convex optimization problem in Hadamard spaces ⋮ Convergence Results for Proximal Point Algorithm in Complete Cat(0) Space for Multivalued Mappings ⋮ Convergence theorems for asymptotically quasi-nonexpansive sequences with applications ⋮ The numerical reckoning of modified proximal point methods for minimization problems in non-positive curvature metric spaces ⋮ Hybrid algorithm with perturbations for total asymptotically non-expansive mappings in CAT(0) space

Uses Software

• UNLocBoX

Cites Work

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