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Convergence analysis of the Fast Subspace Descent method for convex optimization problems
- Source :
- Mathematics of Computation. 89:2249-2282
- Publication Year :
- 2020
- Publisher :
- American Mathematical Society (AMS), 2020.
-
Abstract
- Author(s): Chen, L; Hu, X; Wise, SM | Abstract: The full approximation storage (FAS) scheme is a widely used multigrid method for nonlinear problems. In this paper, a new framework to design and analyze FAS-like schemes for convex optimization problems is developed. The new method, the fast subspace descent (FASD) scheme, which generalizes classical FAS, can be recast as an inexact version of nonlinear multigrid methods based on space decomposition and subspace correction. The local problem in each subspace can be simplified to be linear and one gradient descent iteration (with an appropriate step size) is enough to ensure a global linear (geometric) convergence of FASD for convex optimization problems.
- Subjects :
- Algebra and Number Theory
Applied Mathematics
MathematicsofComputing_NUMERICALANALYSIS
010103 numerical & computational mathematics
01 natural sciences
010101 applied mathematics
Computational Mathematics
Nonlinear system
Multigrid method
Scheme (mathematics)
Convergence (routing)
Convex optimization
Applied mathematics
0101 mathematics
Gradient descent
Subspace topology
Descent (mathematics)
Mathematics
Subjects
Details
- ISSN :
- 10886842 and 00255718
- Volume :
- 89
- Database :
- OpenAIRE
- Journal :
- Mathematics of Computation
- Accession number :
- edsair.doi...........cacf4bd273d34402817e1c64bec04727