On sums and convex combinations of projectors onto convex sets

DOI10.1016/j.jat.2019.02.001zbMath1478.47043arXiv1802.02287OpenAlexW2891945093WikidataQ128316524 ScholiaQ128316524MaRDI QIDQ1740660

Heinz H. Bauschke, Minh N. Bui, Shawn Xianfu Wang

Publication date: 2 May 2019

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

Full work available at URL: https://arxiv.org/abs/1802.02287

zbMATH Keywords

convex combinationmonotone operatorconvex coneconvex setprojection operatorproximity operatorpartial sum propertysum of projectors

Mathematics Subject Classification ID

Convex programming (90C25) Monotone operators and generalizations (47H05) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09) Convex functions and convex programs in convex geometry (52A41) Spaces of linear operators; topological tensor products; approximation properties (46A32) Convex sets and cones of operators (47L07) Convex sets without dimension restrictions (aspects of convex geometry) (52A05)

Related Items

Resolvent and proximal compositions ⋮ Smoothing algorithms for computing the projection onto a Minkowski sum of convex sets

Uses Software

• GeoGebra

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Near equality, near convexity, sums of maximally monotone operators, and averages of firmly nonexpansive mappings
• Calculus on normed vector spaces
• Finding best approximation pairs relative to two closed convex sets in Hilbert spaces
• Monotone operator theory in convex optimization
• The magnitude of the minimal displacement vector for compositions and convex combinations of firmly nonexpansive mappings
• A strongly convergent reflection method for finding the projection onto the intersection of two closed convex sets in a Hilbert space
• The Douglas--Rachford Algorithm for Two (Not Necessarily Intersecting) Affine Subspaces
• Projecting onto the Intersection of a Cone and a Sphere
• Proximité et dualité dans un espace hilbertien
• The Resolvent Order: A Unification of the Orders by Zarantonello, by Loewner, and by Moreau
• Convex analysis and monotone operator theory in Hilbert spaces
• Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations