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Scaled relative graphs: nonexpansive operators via 2D Euclidean geometry
- Source :
- Mathematical Programming. 194:569-619
- Publication Year :
- 2021
- Publisher :
- Springer Science and Business Media LLC, 2021.
-
Abstract
- Many iterative methods in applied mathematics can be thought of as fixed-point iterations, and such algorithms are usually analyzed analytically, with inequalities. In this paper, we present a geometric approach to analyzing contractive and nonexpansive fixed point iterations with a new tool called the scaled relative graph (SRG). The SRG provides a correspondence between nonlinear operators and subsets of the 2D plane. Under this framework, a geometric argument in the 2D plane becomes a rigorous proof of convergence.<br />Published in Mathematical Programming
- Subjects :
- 021103 operations research
Iterative method
Plane (geometry)
General Mathematics
Numerical analysis
0211 other engineering and technologies
010103 numerical & computational mathematics
02 engineering and technology
Fixed point
01 natural sciences
Graph
Optimization and Control (math.OC)
47H05, 47H09, 51M04, 90C25
Convergence (routing)
Euclidean geometry
FOS: Mathematics
Applied mathematics
0101 mathematics
Mathematics - Optimization and Control
Software
Nonlinear operators
Mathematics
Subjects
Details
- ISSN :
- 14364646 and 00255610
- Volume :
- 194
- Database :
- OpenAIRE
- Journal :
- Mathematical Programming
- Accession number :
- edsair.doi.dedup.....2e57a200a5182b53bcdc5c1fd905e7ca