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Incremental proximal methods for large scale convex optimization

We consider the minimization of a sum consisting of a large number of convex component functions f i . For this problem, incremental methods consisting of gradient or subgradient iterations applied to single components have proved very effective. We propose new incremental methods, consisting of pro... Full description

Journal Title: Mathematical programming 2011-06-11, Vol.129 (2), p.163-195
Main Author: Bertsekas, Dimitri P
Format: Electronic Article Electronic Article
Language: English
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Publisher: Berlin/Heidelberg: Springer-Verlag
ID: ISSN: 0025-5610
Link: http://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=24603844
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title: Incremental proximal methods for large scale convex optimization
format: Article
creator:
  • Bertsekas, Dimitri P
subjects:
  • Algorithmics. Computability. Computer arithmetics
  • Algorithms
  • Analysis
  • Applied sciences
  • Approximation
  • Artificial intelligence
  • Calculus of Variations and Optimal Control
  • Optimization
  • Combinatorics
  • Computer science
  • Computer science
  • control theory
  • systems
  • Convergence
  • Convex analysis
  • Electrical engineering
  • Exact sciences and technology
  • Expected values
  • Full Length Paper
  • Iterative methods
  • Laboratories
  • Machine learning
  • Mathematical analysis
  • Mathematical and Computational Physics
  • Mathematical Methods in Physics
  • Mathematical programming
  • Mathematics
  • Mathematics and Statistics
  • Mathematics of Computing
  • Methods
  • Minimization
  • Neural networks
  • Numerical Analysis
  • Operational research and scientific management
  • Operational research. Management science
  • Optimization
  • Randomization
  • Signal processing
  • Studies
  • Theoretical
  • Theoretical computing
ispartof: Mathematical programming, 2011-06-11, Vol.129 (2), p.163-195
description: We consider the minimization of a sum consisting of a large number of convex component functions f i . For this problem, incremental methods consisting of gradient or subgradient iterations applied to single components have proved very effective. We propose new incremental methods, consisting of proximal iterations applied to single components, as well as combinations of gradient, subgradient, and proximal iterations. We provide a convergence and rate of convergence analysis of a variety of such methods, including some that involve randomization in the selection of components. We also discuss applications in a few contexts, including signal processing and inference/machine learning.
language: eng
source:
identifier: ISSN: 0025-5610
fulltext: no_fulltext
issn:
  • 0025-5610
  • 1436-4646
url: Link


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descriptionWe consider the minimization of a sum consisting of a large number of convex component functions f i . For this problem, incremental methods consisting of gradient or subgradient iterations applied to single components have proved very effective. We propose new incremental methods, consisting of proximal iterations applied to single components, as well as combinations of gradient, subgradient, and proximal iterations. We provide a convergence and rate of convergence analysis of a variety of such methods, including some that involve randomization in the selection of components. We also discuss applications in a few contexts, including signal processing and inference/machine learning.
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subjectAlgorithmics. Computability. Computer arithmetics ; Algorithms ; Analysis ; Applied sciences ; Approximation ; Artificial intelligence ; Calculus of Variations and Optimal Control; Optimization ; Combinatorics ; Computer science ; Computer science; control theory; systems ; Convergence ; Convex analysis ; Electrical engineering ; Exact sciences and technology ; Expected values ; Full Length Paper ; Iterative methods ; Laboratories ; Machine learning ; Mathematical analysis ; Mathematical and Computational Physics ; Mathematical Methods in Physics ; Mathematical programming ; Mathematics ; Mathematics and Statistics ; Mathematics of Computing ; Methods ; Minimization ; Neural networks ; Numerical Analysis ; Operational research and scientific management ; Operational research. Management science ; Optimization ; Randomization ; Signal processing ; Studies ; Theoretical ; Theoretical computing
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descriptionWe consider the minimization of a sum consisting of a large number of convex component functions f i . For this problem, incremental methods consisting of gradient or subgradient iterations applied to single components have proved very effective. We propose new incremental methods, consisting of proximal iterations applied to single components, as well as combinations of gradient, subgradient, and proximal iterations. We provide a convergence and rate of convergence analysis of a variety of such methods, including some that involve randomization in the selection of components. We also discuss applications in a few contexts, including signal processing and inference/machine learning.
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abstractWe consider the minimization of a sum consisting of a large number of convex component functions f i . For this problem, incremental methods consisting of gradient or subgradient iterations applied to single components have proved very effective. We propose new incremental methods, consisting of proximal iterations applied to single components, as well as combinations of gradient, subgradient, and proximal iterations. We provide a convergence and rate of convergence analysis of a variety of such methods, including some that involve randomization in the selection of components. We also discuss applications in a few contexts, including signal processing and inference/machine learning.
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