MONOTONE OPERATORS AND THE PROXIMAL POINT ALGORITHM IN COMPLETE CAT(0) METRIC SPACES

DOI10.1017/S1446788716000446zbMath1489.47093OpenAlexW2523198149MaRDI QIDQ4591204

Hadi Khatibzadeh, Sajad Ranjbar

Publication date: 13 November 2017

Published in: Journal of the Australian Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s1446788716000446

zbMATH Keywords

nonexpansive mappingmonotone operatorsubdifferentialHadamard spaceproximal point algorithm\(\Delta\)-convergence

Mathematics Subject Classification ID

Numerical mathematical programming methods (65K05) Monotone operators and generalizations (47H05) Iterative procedures involving nonlinear operators (47J25) Special maps on metric spaces (54E40)

Related Items

Viscosity approximation methods for monotone inclusion and fixed point problems in CAT(0) space ⋮ A modified viscosity implicit-type proximal point algorithm for monotone inclusions and asymptotically nonexpansive mappings in Hadamard spaces ⋮ Approximating common fixed points of a family of non-self mappings in CAT(0) spaces ⋮ Strong and \(\Delta\)-convergence to a zero of a monotone operator in CAT(0) spaces ⋮ Approximating a Solution of the Inclusion Problem for an Infinite Family of Monotone Operators in Hadamard Spaces and Its Applications ⋮ A proximal point algorithm for finding minimizers and fixed points of quasi-pseudo-contractive mappings in CAT(0) spaces ⋮ Approximation of common solution of finite family of monotone inclusion and fixed point problems for demicontractive multivalued mappings in CAT(0) spaces ⋮ Strong convergence theorems for fixed point of multi-valued mappings in Hadamard spaces ⋮ Proximal point methods with possible unbounded errors for monotone operators in Hadamard spaces ⋮ An extragradient algorithm for solving equilibrium problem and zero point problem in Hadamard spaces ⋮ Mean ergodic theorems for a sequence of nonexpansive mappings in complete \(\mathrm{CAT}(0)\) spaces and its applications ⋮ A viscosity iterative algorithm for a family of monotone inclusion problems in an Hadamard space ⋮ A modified viscosity iterative method for implicit midpoint rule for optimization and fixed point problems in CAT(0) spaces ⋮ Convergence theorems for monotone vector field inclusions and minimization problems in Hadamard spaces ⋮ On \(\theta\)-generalized demimetric mappings and monotone operators in Hadamard spaces ⋮ Viscosity approximation method for fixed point of pseudocontraction mapping in Hadamard spaces ⋮ Iterative approaches for solving equilibrium problems, zero point problems and fixed point problems in Hadamard spaces ⋮ Halpern-type proximal point Algorithm in \(\mathrm{CAT}(0)\) spaces ⋮ On the zero point problem of monotone operators in Hadamard spaces ⋮ Iterative algorithm for a family of monotone inclusion problems in cat(0) spaces ⋮ Multi-step iterative algorithm for minimization and fixed point problems in \(p\)-uniformly convex metric spaces ⋮ The strong convergence of a proximal point algorithm in complete CAT(0) metric spaces ⋮ On the proximal point algorithm and demimetric mappings in \(\mathrm{CAT}(0)\) spaces ⋮ Iterative algorithm for a family of generalized strictly pseudononspreading mappings in CAT(0) spaces ⋮ Monotone inclusion problem and fixed point problem of a generalized demimetric mapping in CAT(0) spaces ⋮ Strong convergence theorem for monotone inclusion problem in CAT(0) spaces ⋮ A strong convergence theorem for monotone inclusion and minimization problems in complete CAT(0) spaces ⋮ Viscosity iterative techniques for approximating a common zero of monotone operators in an Hadamard space ⋮ On the strong convergence of a modified Halpern algorithm in a CAT(0) space ⋮ Modified proximal point methods involving quasi-pseudocontractive mappings in Hadamard spaces ⋮ Monotone Vector Fields and Generation of Nonexpansive Semigroups in Complete CAT(0) Spaces ⋮ Unnamed Item ⋮ Monotone relations in Hadamard spaces ⋮ Modified shrinking projection methods in CAT(0) space ⋮ Strong convergence theorem for family of minimization and monotone inclusion problems in Hadamard spaces

Cites Work

• On the convergence of inexact proximal point algorithm on Hadamard manifolds
• Duality and subdifferential for convex functions on complete \(CAT(0)\) metric spaces
• A concept of convergence in geodesic spaces
• On the proximal point algorithm
• CAT\((k)\)-spaces, weak convergence and fixed points
• Produits infinis de resolvantes
• The proximal point algorithm in metric spaces
• On \(\Delta\)-convergence theorems in CAT\((0)\) spaces
• Quasilinearization and curvature of Aleksandrov spaces
• Monotone vector fields and the proximal point algorithm on Hadamard manifolds
• On the Convergence of the Proximal Point Algorithm for Convex Minimization
• Remarks on Some Fixed Point Theorems
• Monotone Operators and the Proximal Point Algorithm
• Weak topologies in complete $CAT(0)$ metric spaces
• Convergence of nonlinear semigroups under nonpositive curvature
• Metric structures for Riemannian and non-Riemannian spaces. Transl. from the French by Sean Michael Bates. With appendices by M. Katz, P. Pansu, and S. Semmes. Edited by J. LaFontaine and P. Pansu
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item