NON-STRICTLY CONVEX MINIMIZATION OVER THE FIXED POINT SET OF AN ASYMPTOTICALLY SHRINKING NONEXPANSIVE MAPPING

By Nobuhiko Ogura, Isao Yamada. 2002

79 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/dd5fc00f35080929abd6cd5e6e2086498a618acc

How researchers see this paper

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

In Applied Mathematics

In Computational Theory and Mathematics

In Mathematical Physics

Citations in the corpus

A Primal–Dual Splitting Method for Convex Optimization Involving Lipschitzian, Proximable and Linear Composite Terms (2012, background): “He also thanks Isao Yamada for pointing out his article [39], which allowed to improve Lemma 4.”
Compositions and convex combinations of averaged nonexpansive operators (2014, background): “As discussed in [6,11,16], averaged operators are stable under compositions and convex combinations and such operations form basic building blocks in various composite fixed point algorithms.”
Adaptive Projected Subgradient Method for Asymptotic Minimization of Sequence of Nonnegative Convex Functions (2005, methodology): “The following proposition is deduced in ways similar to discussion on nonexpansive mapping in Bauschke and Borwein (1996) and Ogura and Yamada (2002).”
The Adaptive Projected Subgradient Method over the Fixed Point Set of Strongly Attracting Nonexpansive Mappings (2006, unknown): “(1 − t ) T 1 + tT 2 is ((1 − t )α 1 + t α 2 )-averaged nonexpansive, ∀ t ∈ [0, 1] [ 25 ].”
Methods for Variational Inequality Problem Over the Intersection of Fixed Point Sets of Quasi-Nonexpansive Operators (2013, methodology): “The method and its extensions [24, 25, 33] inspired many researcher to active studies on related algorithms (see, e.”
Hybrid Steepest Descent Method for Variational Inequality Problem over the Fixed Point Set of Certain Quasi-nonexpansive Mappings (2005, methodology): “Then it follows that 1+ 2−2 1 2 1− 1 2 ∈ 0 1 and T1T2 is 1+ 2−2 1 2 1− 1 2 -averaged nonexpansive (see Ogura and Yamada, 2002).”
Plug-and-Play Methods Provably Converge with Properly Trained Denoisers (2019, unknown): “An mapping Lemma 5 ((Ogura & Yamada, 2002; Combettes & Yamada, 2015)) .”