On Uniform Convexity, Total Convexity and Convergence of the Proximal Point and Outer Bregman Projection Algorithms in Banach Spaces

87 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Weak Convergence of Orbits of Nonlinear Operators in Reflexive Banach Spaces (2003, background): “Taking into account [Butnariu et al., 2003, Proposition 2.4], it follows that if X is a locally uniformly convex Banach space (as many spaces happen to be—see Diestel (1975)), then all the functions f p¼k kp with p2 (1,1) are totally convex on X and, therefore, satisfy (A1) no matter how K is…”
Two Strong Convergence Theorems for a Proximal Method in Reflexive Banach Spaces (2010, unknown): “See, for example, [5, 6, 7, 10, 11, 15, 16, 19, 21, 22, 25, 26, 29, 30, 32, 33, 35, 39, 41, 43].”
Uniformly convex functions on Banach spaces (2008, background): “Additionally, related properties of convex functions and their applications have been studied in papers such as [2, 3, 4, 5].”
Signal Recovery by Proximal Forward-Backward Splitting (2005, background): “Examples of functions satisfying the various types of uniform convexity deﬁned above can be found in [12, 75].”
Bregman Monotone Optimization Algorithms (2003, unknown): “E-mail: plc@math.jussieu.fr.”