Monotone Vector Fields and Generation of Nonexpansive Semigroups in Complete CAT(0) Spaces

DOI10.1080/01630563.2021.1931879zbMath1482.90222arXiv1906.05984OpenAlexW3172261118MaRDI QIDQ5009117

Parin Chaipunya, Fumiaki Kohsaka, Poom Kumam

Publication date: 19 August 2021

Published in: Numerical Functional Analysis and Optimization (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1906.05984

zbMATH Keywords

resolventnonexpansive semigroupYosida approximationtangent spacemonotone vector field

Mathematics Subject Classification ID

Variational inequalities (49J40) Monotone operators and generalizations (47H05) Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) (90C33) Numerical methods for variational inequalities and related problems (65K15)

Related Items

A differential perspective on gradient flows on \(\mathbf{\mathsf{CAT}} (\kappa)\)-spaces and applications ⋮ Mean ergodic theorems for a sequence of nonexpansive mappings in complete \(\mathrm{CAT}(0)\) spaces and its applications ⋮ Convergence theorems for monotone vector field inclusions and minimization problems in Hadamard spaces ⋮ Iterative approximation of a common solution of split equilibrium, split variational inequality, and fixed point problem for a nonexpansive semigroup ⋮ Basic Convex Analysis in Metric Spaces with Bounded Curvature

Cites Work

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• Asymptotic behavior of averaged and firmly nonexpansive mappings in geodesic spaces
• Monotone and accretive vector fields on Riemannian manifolds
• Convergence of a sequence of sets in a Hadamard space and the shrinking projection method for a real Hilbert ball
• Duality and subdifferential for convex functions on complete \(CAT(0)\) metric spaces
• A concept of convergence in geodesic spaces
• Gradient flows on nonpositively curved metric spaces and harmonic maps
• The tangent cone of an Aleksandrov space of curvature \(\leq K\)
• Monotonicity, resolvents and Yosida approximations of operators on Hilbert manifolds.
• Convex functionals and generalized harmonic maps into spaces of non positive curvature
• The proximal point algorithm in metric spaces
• Backward-backward splitting in Hadamard spaces
• Fixed points of uniformly Lipschitzian mappings
• Convex analysis and optimization in Hadamard spaces
• Approximation for convex functionals on non-positively curved spaces and the Trotter–Kato product formula
• Firmly nonexpansive mappings in classes of geodesic spaces
• Monotone vector fields and the proximal point algorithm on Hadamard manifolds
• MONOTONE OPERATORS AND THE PROXIMAL POINT ALGORITHM IN COMPLETE CAT(0) METRIC SPACES
• On the proximal point method in Hadamard spaces
• Weak topologies in complete $CAT(0)$ metric spaces
• Generation of Semi-Groups of Nonlinear Transformations on General Banach Spaces