The continuity of metric projections as functions of the data

DOI10.1016/0021-9045(74)90065-3zbMath0297.41021OpenAlexW1974283430MaRDI QIDQ1214068

James W. Daniel

Publication date: 1974

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0021-9045(74)90065-3

Mathematics Subject Classification ID

Best approximation, Chebyshev systems (41A50) Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65)

Related Items

Uniform convexity and the splitting problem for selections ⋮ Stability estimates of continuous selections for metric almost-projections ⋮ Stability of minimization problems and the error bound condition ⋮ Properties of the metric projection on weakly Vial-convex sets and parametrization of set-valued mappings with weakly convex images ⋮ Distance function associated to a prox-regular set ⋮ Dynamical system related to primal-dual splitting projection methods ⋮ The Lipschitz property of the metric projection in the Hilbert space ⋮ Criterion for the existence of a 1-Lipschitz selection from the metric projection onto the set of continuous selections from a multivalued mapping ⋮ Continuous dependence of an element realizing the minimum of a convex functional on the set of admissible elements ⋮ Unnamed Item ⋮ On the splitting problem for selections

Cites Work

• Bounds for error in the solution set of a perturbed linear program
• Global approximation of a compact set by elements of a convex set in a normed space
• Perturbations of best approximation problems
• Stability of the solution of definite quadratic programs
• On $L_1 $ Approximation I: Computation for Continuous Functions and Continuous Dependence
• Normed Convex Processes
• On Perturbations in Systems of Linear Inequalities
• Unnamed Item
• Unnamed Item
• Unnamed Item