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Local convergence of tensor methods
- Source :
- Mathematical Programming, Vol. 193, no. 1, p. 315-336 (2022), Mathematical Programming
- Publication Year :
- 2019
-
Abstract
- In this paper, we study local convergence of high-order Tensor Methods for solving convex optimization problems with composite objective. We justify local superlinear convergence under the assumption of uniform convexity of the smooth component, having Lipschitz-continuous high-order derivative. The convergence both in function value and in the norm of minimal subgradient is established. Global complexity bounds for the Composite Tensor Method in convex and uniformly convex cases are also discussed. Lastly, we show how local convergence of the methods can be globalized using the inexact proximal iterations.
- Subjects :
- TheoryofComputation_MISCELLANEOUS
90C25, 90C06, 65K05
General Mathematics
0211 other engineering and technologies
MathematicsofComputing_NUMERICALANALYSIS
010103 numerical & computational mathematics
02 engineering and technology
Proximal methods
01 natural sciences
Convexity
High-order methods
Tensor methods
Tensor (intrinsic definition)
Convergence (routing)
FOS: Mathematics
Applied mathematics
0101 mathematics
Local convergence
Mathematics - Optimization and Control
Subgradient method
Mathematics
021103 operations research
Regular polygon
Function (mathematics)
Convex optimization
Optimization and Control (math.OC)
Uniform convexity
Software
Subjects
Details
- ISSN :
- 00255610
- Volume :
- 193
- Issue :
- 1
- Database :
- OpenAIRE
- Journal :
- Mathematical programming
- Accession number :
- edsair.doi.dedup.....d6f0724a9969c71bb4acb1774f6b8928