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Contracting Proximal Methods for Smooth Convex Optimization
- Source :
- SIAM Journal on Optimization, Vol. 30, no.4, p. 3146-3169 (2020), SIAM Journal on Optimization
- Publication Year :
- 2020
- Publisher :
- Society for Industrial & Applied Mathematics (SIAM), 2020.
-
Abstract
- In this paper, we propose new accelerated methods for smooth convex optimization, called contracting proximal methods. At every step of these methods, we need to minimize a contracted version of the objective function augmented by a regularization term in the form of Bregman divergence. We provide global convergence analysis for a general scheme admitting inexactness in solving the auxiliary subproblem. In the case of using for this purpose high-order tensor methods, we demonstrate an acceleration effect for both convex and uniformly convex composite objective functions. Thus, our construction explains acceleration for methods of any order starting from one. The augmentation of the number of calls of oracle due to computing the contracted proximal steps is limited by the logarithmic factor in the worst-case complexity bound.
- Subjects :
- high-order algorithms
Mathematical optimization
49M15, 49M37, 65K05, 90C25, 90C30
021103 operations research
global complexity bounds
0211 other engineering and technologies
proximal method
010103 numerical & computational mathematics
02 engineering and technology
01 natural sciences
Convex optimization
Theoretical Computer Science
accelerated methods
Optimization and Control (math.OC)
FOS: Mathematics
0101 mathematics
Mathematics - Optimization and Control
Software
Mathematics
Subjects
Details
- ISSN :
- 10957189 and 10526234
- Volume :
- 30
- Database :
- OpenAIRE
- Journal :
- SIAM Journal on Optimization
- Accession number :
- edsair.doi.dedup.....92b7b18087d9d9cdc17af478e6af7b14