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Convex analysis and optimization in Hadamard spaces /

Bibliographic Details
Main Author: Bacák, Miroslav
Corporate Author: EBSCOhost
Format: eBook
Language:English
Published: Berlin ; Boston : Walter de Gruyter GmbH & Co. KG, [2014]
Series:De Gruyter series in nonlinear analysis and applications ; 22.
Subjects:
Metric spaces.
G-spaces.
Hadamard matrices.
Electronic books.
Online Access:Connect to the full text of this electronic book
Table of Contents:
  • 1. Geometry of nonpositive curvature
  • 1.1. Geodesic metric spaces
  • 1.2. Meet Hadamard spaces
  • 1.3. Equivalent conditions for CAT(0)
  • 2. Convex sets and convex functions
  • 2.1. Convex sets
  • 2.2. Convex functions
  • 2.3. Convexity and probability measures
  • 3. Weak convergence in Hadamard spaces
  • 3.1. Existence of weak limits
  • 3.2. Weak convergence and convexity
  • 3.3. An application in fixed point theory
  • 4. Nonexpansive mappings
  • 4.1. Kirszbraun-Valentine extension
  • 4.2. Resolvent of a nonexpansive mapping
  • 4.3. Strongly continuous semigroup
  • 5. Gradient flow of a convex functional
  • 5.1. Gradient flow semigroup
  • 5.2. Mosco convergence and its consequences
  • 5.3. Lie-Trotter-Kato formula
  • 6. Convex optimization algorithms
  • 6.1. Convex feasibility problems
  • 6.2. Fixed point approximations
  • 6.3. Proximal point algorithm
  • 7. Probabilistic tools in Hadamard spaces
  • 7.1. Random variables and expectations
  • 7.2. Law of large numbers
  • 7.3. Conditional expectations
  • 8. Tree space and its applications
  • 8.1. Construction of the BHV tree space
  • 8.2. Owen-Provan algorithm
  • 8.3. Medians and means of trees.