About the Lipschitz property of the metric projection in the Hilbert space

DOI10.1016/j.jmaa.2012.05.024zbMath1253.46075OpenAlexW2068302914MaRDI QIDQ442476

Maxim V. Balashov, Maxim O. Golubev

Publication date: 1 August 2012

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2012.05.024

zbMATH Keywords

Hilbert spaceLipschitz conditiongradient projection algorithmdistance functionmetric projectionMazur intersection propertystrongly convex set

Mathematics Subject Classification ID

Convex programming (90C25) Geometry and structure of normed linear spaces (46B20) Characterizations of Hilbert spaces (46C15) Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65) Applications of functional analysis in optimization, convex analysis, mathematical programming, economics (46N10)

Related Items (10)

Maximization of a function with Lipschitz continuous gradient ⋮ Gradient methods on strongly convex feasible sets and optimal control of affine systems ⋮ Finite element approximation of dielectrophoretic force driven flow problems ⋮ Approximating properties of metric and generalized metric projections in uniformly convex and uniformly smooth Banach spaces ⋮ The Glowinski-Le Tallec splitting method revisited in the framework of equilibrium problems in Hilbert spaces ⋮ The Lipschitz property of the metric projection in the Hilbert space ⋮ The gradient projection algorithm for a proximally smooth set and a function with Lipschitz continuous gradient ⋮ Unnamed Item ⋮ Unnamed Item ⋮ The gradient projection algorithm for smooth sets and functions in nonconvex case

Cites Work

• The Lipschitz continuity of the metric projection
• Uniformly convex subsets of the Hilbert space with modulus of convexity of the second order
• Introductory lectures on convex optimization. A basic course.
• Convex bodies of constant width
• On nonlinear projections in Banach spaces
• Strong and Weak Convexity of Sets and Functions
• Strongly convex analysis
• Characterizations of reflexivity
• Adjoint Transform, Overconvexity and Sets of Constant Width
• Characterisation of normed linear spaces with Mazur's intersection property
• $ M$-strongly convex subsets and their generating sets
• Über schwache Konvergenz in den Raümen ($L^{p}$)
• Weakly convex and proximally smooth sets in Banach spaces
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