Compositions and Convex Combinations of Averaged Nonexpansive Operators
Patrick L. Combettes, Isao Yamada
TL;DR
This paper studies how compositions and convex combinations of averaged nonexpansive operators behave and uses these properties to develop new fixed point algorithms in Hilbert spaces, including an extended forward-backward splitting method.
Contribution
It introduces new theoretical insights into averaged nonexpansive operators and proposes an extended forward-backward splitting algorithm for monotone operator problems.
Findings
Properties of compositions and convex combinations are characterized.
An extended forward-backward splitting algorithm is developed.
New fixed point algorithms are proposed for Hilbert spaces.
Abstract
Properties of compositions and convex combinations of averaged nonexpansive operators are investigated and applied to the design of new fixed point algorithms in Hilbert spaces. An extended version of the forward-backward splitting algorithm for finding a zero of the sum of two monotone operators is obtained.
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Taxonomy
TopicsOptimization and Variational Analysis · Fixed Point Theorems Analysis · Advanced Optimization Algorithms Research