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An optimal variant of Kelley’s cutting-plane method

We propose a new variant of Kelley’s cutting-plane method for minimizing a nonsmooth convex Lipschitz-continuous function over the Euclidean space. We derive the method through a constructive approach and prove that it attains the optimal rate of convergence for this class of problems.

Journal Title: Mathematical programming 2016, Vol.160 (1-2), p.321-351
Main Author: Drori, Yoel
Other Authors: Teboulle, Marc
Format: Electronic Article Electronic Article
Language: English
Subjects:
Publisher: Berlin/Heidelberg: Springer Berlin Heidelberg
ID: ISSN: 0025-5610
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title: An optimal variant of Kelley’s cutting-plane method
format: Article
creator:
  • Drori, Yoel
  • Teboulle, Marc
subjects:
  • Accuracy
  • Algorithms
  • Calculus of Variations and Optimal Control
  • Optimization
  • Combinatorics
  • Construction methods
  • Convergence
  • Convex analysis
  • Euclidean geometry
  • Full Length Paper
  • Functions (mathematics)
  • Mathematical analysis
  • Mathematical and Computational Physics
  • Mathematical Methods in Physics
  • Mathematical programming
  • Mathematics
  • Mathematics and Statistics
  • Mathematics of Computing
  • Methods
  • Numerical Analysis
  • Optimization
  • Studies
  • Theoretical
  • Topological manifolds
ispartof: Mathematical programming, 2016, Vol.160 (1-2), p.321-351
description: We propose a new variant of Kelley’s cutting-plane method for minimizing a nonsmooth convex Lipschitz-continuous function over the Euclidean space. We derive the method through a constructive approach and prove that it attains the optimal rate of convergence for this class of problems.
language: eng
source:
identifier: ISSN: 0025-5610
fulltext: no_fulltext
issn:
  • 0025-5610
  • 1436-4646
url: Link


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descriptionWe propose a new variant of Kelley’s cutting-plane method for minimizing a nonsmooth convex Lipschitz-continuous function over the Euclidean space. We derive the method through a constructive approach and prove that it attains the optimal rate of convergence for this class of problems.
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subjectAccuracy ; Algorithms ; Calculus of Variations and Optimal Control; Optimization ; Combinatorics ; Construction methods ; Convergence ; Convex analysis ; Euclidean geometry ; Full Length Paper ; Functions (mathematics) ; Mathematical analysis ; Mathematical and Computational Physics ; Mathematical Methods in Physics ; Mathematical programming ; Mathematics ; Mathematics and Statistics ; Mathematics of Computing ; Methods ; Numerical Analysis ; Optimization ; Studies ; Theoretical ; Topological manifolds
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descriptionWe propose a new variant of Kelley’s cutting-plane method for minimizing a nonsmooth convex Lipschitz-continuous function over the Euclidean space. We derive the method through a constructive approach and prove that it attains the optimal rate of convergence for this class of problems.
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abstractWe propose a new variant of Kelley’s cutting-plane method for minimizing a nonsmooth convex Lipschitz-continuous function over the Euclidean space. We derive the method through a constructive approach and prove that it attains the optimal rate of convergence for this class of problems.
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