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An Approximate Quasi-Newton Bundle-Type Method for Nonsmooth Optimization

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Zeitschriftentitel: Abstract and Applied Analysis
Personen und Körperschaften: Shen, Jie, Pang, Li-Ping, Li, Dan
In: Abstract and Applied Analysis, 2013, 2013, S. 1-7
Medientyp: E-Article
Sprache: Englisch
veröffentlicht:
Hindawi Limited
Schlagwörter:
author_facet Shen, Jie
Pang, Li-Ping
Li, Dan
Shen, Jie
Pang, Li-Ping
Li, Dan
author Shen, Jie
Pang, Li-Ping
Li, Dan
spellingShingle Shen, Jie
Pang, Li-Ping
Li, Dan
Abstract and Applied Analysis
An Approximate Quasi-Newton Bundle-Type Method for Nonsmooth Optimization
Applied Mathematics
Analysis
author_sort shen, jie
spelling Shen, Jie Pang, Li-Ping Li, Dan 1085-3375 1687-0409 Hindawi Limited Applied Mathematics Analysis http://dx.doi.org/10.1155/2013/697474 <jats:p>An implementable algorithm for solving a nonsmooth convex optimization problem is proposed by combining Moreau-Yosida regularization and bundle and quasi-Newton ideas. In contrast with quasi-Newton bundle methods of Mifflin et al. (1998), we only assume that the values of the objective function and its subgradients are evaluated approximately, which makes the method easier to implement. Under some reasonable assumptions, the proposed method is shown to have a Q-superlinear rate of convergence.</jats:p> An Approximate Quasi-Newton Bundle-Type Method for Nonsmooth Optimization Abstract and Applied Analysis
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series Abstract and Applied Analysis
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title An Approximate Quasi-Newton Bundle-Type Method for Nonsmooth Optimization
title_unstemmed An Approximate Quasi-Newton Bundle-Type Method for Nonsmooth Optimization
title_full An Approximate Quasi-Newton Bundle-Type Method for Nonsmooth Optimization
title_fullStr An Approximate Quasi-Newton Bundle-Type Method for Nonsmooth Optimization
title_full_unstemmed An Approximate Quasi-Newton Bundle-Type Method for Nonsmooth Optimization
title_short An Approximate Quasi-Newton Bundle-Type Method for Nonsmooth Optimization
title_sort an approximate quasi-newton bundle-type method for nonsmooth optimization
topic Applied Mathematics
Analysis
url http://dx.doi.org/10.1155/2013/697474
publishDate 2013
physical 1-7
description <jats:p>An implementable algorithm for solving a nonsmooth convex optimization problem is proposed by combining Moreau-Yosida regularization and bundle and quasi-Newton ideas. In contrast with quasi-Newton bundle methods of Mifflin et al. (1998), we only assume that the values of the objective function and its subgradients are evaluated approximately, which makes the method easier to implement. Under some reasonable assumptions, the proposed method is shown to have a Q-superlinear rate of convergence.</jats:p>
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author Shen, Jie, Pang, Li-Ping, Li, Dan
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author_sort shen, jie
container_start_page 1
container_title Abstract and Applied Analysis
container_volume 2013
description <jats:p>An implementable algorithm for solving a nonsmooth convex optimization problem is proposed by combining Moreau-Yosida regularization and bundle and quasi-Newton ideas. In contrast with quasi-Newton bundle methods of Mifflin et al. (1998), we only assume that the values of the objective function and its subgradients are evaluated approximately, which makes the method easier to implement. Under some reasonable assumptions, the proposed method is shown to have a Q-superlinear rate of convergence.</jats:p>
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publishDate 2013
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source_id 49
spelling Shen, Jie Pang, Li-Ping Li, Dan 1085-3375 1687-0409 Hindawi Limited Applied Mathematics Analysis http://dx.doi.org/10.1155/2013/697474 <jats:p>An implementable algorithm for solving a nonsmooth convex optimization problem is proposed by combining Moreau-Yosida regularization and bundle and quasi-Newton ideas. In contrast with quasi-Newton bundle methods of Mifflin et al. (1998), we only assume that the values of the objective function and its subgradients are evaluated approximately, which makes the method easier to implement. Under some reasonable assumptions, the proposed method is shown to have a Q-superlinear rate of convergence.</jats:p> An Approximate Quasi-Newton Bundle-Type Method for Nonsmooth Optimization Abstract and Applied Analysis
spellingShingle Shen, Jie, Pang, Li-Ping, Li, Dan, Abstract and Applied Analysis, An Approximate Quasi-Newton Bundle-Type Method for Nonsmooth Optimization, Applied Mathematics, Analysis
title An Approximate Quasi-Newton Bundle-Type Method for Nonsmooth Optimization
title_full An Approximate Quasi-Newton Bundle-Type Method for Nonsmooth Optimization
title_fullStr An Approximate Quasi-Newton Bundle-Type Method for Nonsmooth Optimization
title_full_unstemmed An Approximate Quasi-Newton Bundle-Type Method for Nonsmooth Optimization
title_short An Approximate Quasi-Newton Bundle-Type Method for Nonsmooth Optimization
title_sort an approximate quasi-newton bundle-type method for nonsmooth optimization
title_unstemmed An Approximate Quasi-Newton Bundle-Type Method for Nonsmooth Optimization
topic Applied Mathematics, Analysis
url http://dx.doi.org/10.1155/2013/697474