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An Approximate Quasi-Newton Bundle-Type Method for Nonsmooth Optimization
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Zeitschriftentitel: | Abstract and Applied Analysis |
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Personen und Körperschaften: | , , |
In: | Abstract and Applied Analysis, 2013, 2013, S. 1-7 |
Medientyp: | E-Article |
Sprache: | Englisch |
veröffentlicht: |
Hindawi Limited
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Schlagwörter: |
author_facet |
Shen, Jie Pang, Li-Ping Li, Dan Shen, Jie Pang, Li-Ping Li, Dan |
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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 |
doi_str_mv |
10.1155/2013/697474 |
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Hindawi Limited, 2013 |
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Hindawi Limited, 2013 |
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1085-3375 1687-0409 |
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1085-3375 1687-0409 |
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2013 |
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Hindawi Limited |
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ai |
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Abstract and Applied Analysis |
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49 |
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 |
author_facet | Shen, Jie, Pang, Li-Ping, Li, Dan, Shen, Jie, Pang, Li-Ping, Li, Dan |
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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id | ai-49-aHR0cDovL2R4LmRvaS5vcmcvMTAuMTE1NS8yMDEzLzY5NzQ3NA |
imprint | Hindawi Limited, 2013 |
imprint_str_mv | Hindawi Limited, 2013 |
institution | DE-Pl11, DE-Rs1, DE-105, DE-14, DE-Ch1, DE-L229, DE-D275, DE-Bn3, DE-Brt1, DE-D161, DE-Zwi2, DE-Gla1, DE-Zi4, DE-15 |
issn | 1085-3375, 1687-0409 |
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language | English |
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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 |