Implicit error bounds for Picard iterations on Hilbert spaces
From MaRDI portal
Publication:1639952
DOI10.1007/s10013-018-0279-xzbMath1391.49025OpenAlexW2793942190MaRDI QIDQ1639952
D. Russell Luke, Matthew K. Tam, H. Thao Nguyen
Publication date: 13 June 2018
Published in: Vietnam Journal of Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s10013-018-0279-x
fixed pointsstrong convergenceerror boundsPicard iterationmetric regularitymetric subregularitynonexpansivenessaveraged operators
Numerical mathematical programming methods (65K05) Nonlinear programming (90C30) Numerical optimization and variational techniques (65K10) Numerical methods based on necessary conditions (49M05) Set-valued and variational analysis (49J53) Decomposition methods (49M27)
Related Items
Characterizations of stability of error bounds for convex inequality constraint systems ⋮ Linear convergence rates for extrapolated fixed point algorithms ⋮ Convergence rates for boundedly regular systems ⋮ Asymptotic regularity, fixed points and successive approximations
Cites Work
- Unnamed Item
- On local convergence of the method of alternating projections
- Nonlinear regularity models
- Linear and strong convergence of algorithms involving averaged nonexpansive operators
- A dynamical system associated with the fixed points set of a nonexpansive operator
- Transversality and alternating projections for nonconvex sets
- Metric subregularity and the proximal point method
- Error bounds for the method of alternating projections
- An example concerning fixed points
- On the convergence of von Neumann's alternating projection algorithm for two sets
- From error bounds to the complexity of first-order descent methods for convex functions
- An alternating projection that does not converge in norm
- Error bounds for parametric polynomial systems with applications to higher-order stability analysis and convergence rates
- Convergence Rate Analysis for Averaged Fixed Point Iterations in Common Fixed Point Problems
- Characterizing arbitrarily slow convergence in the method of alternating projections
- On the Convergence of the Proximal Point Algorithm for Convex Minimization
- Fixed Points and Iteration of a Nonexpansive Mapping in a Banach Space
- Accelerating the convergence of the method of alternating projections
- Analysis of the Convergence Rate for the Cyclic Projection Algorithm Applied to Basic Semialgebraic Convex Sets
- Weak convergence of the sequence of successive approximations for nonexpansive mappings
- Functional Operators (AM-21), Volume 1
- Convex analysis and monotone operator theory in Hilbert spaces