A primal-dual algorithm framework for convex saddle-point optimization

Abstract In this study, we introduce a primal-dual prediction-correction algorithm framework for convex optimization problems with known saddle-point structure. Our unified frame adds the proximal term with a positive definite weighting matrix. Moreover, different proximal parameters in the frame ca...
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Gespeichert in:

Autor*in:	Zhang, Benxin [verfasserIn] Zhu, Zhibin [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2017

Schlagwörter:	primal-dual method proximal point algorithm convex optimization variational inequalities

Übergeordnetes Werk:	Enthalten in: Journal of inequalities and applications - Heidelberg : Springer, 2005, 2017(2017), 1 vom: 25. Okt.
Übergeordnetes Werk:	volume:2017 ; year:2017 ; number:1 ; day:25 ; month:10

Links:	Volltext

DOI / URN:	10.1186/s13660-017-1548-z

Katalog-ID:	SPR032566255

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spelling	10.1186/s13660-017-1548-z doi (DE-627)SPR032566255 (SPR)s13660-017-1548-z-e DE-627 ger DE-627 rakwb eng 510 ASE 31.49 bkl Zhang, Benxin verfasserin aut A primal-dual algorithm framework for convex saddle-point optimization 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In this study, we introduce a primal-dual prediction-correction algorithm framework for convex optimization problems with known saddle-point structure. Our unified frame adds the proximal term with a positive definite weighting matrix. Moreover, different proximal parameters in the frame can derive some existing well-known algorithms and yield a class of new primal-dual schemes. We prove the convergence of the proposed frame from the perspective of proximal point algorithm-like contraction methods and variational inequalities approach. The convergence rate $O(1/t)$ in the ergodic and nonergodic senses is also given, where t denotes the iteration number. primal-dual method (dpeaa)DE-He213 proximal point algorithm (dpeaa)DE-He213 convex optimization (dpeaa)DE-He213 variational inequalities (dpeaa)DE-He213 Zhu, Zhibin verfasserin aut Enthalten in Journal of inequalities and applications Heidelberg : Springer, 2005 2017(2017), 1 vom: 25. Okt. (DE-627)320977056 (DE-600)2028512-7 1029-242X nnns volume:2017 year:2017 number:1 day:25 month:10 https://dx.doi.org/10.1186/s13660-017-1548-z kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2027 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 31.49 ASE AR 2017 2017 1 25 10
allfields_unstemmed	10.1186/s13660-017-1548-z doi (DE-627)SPR032566255 (SPR)s13660-017-1548-z-e DE-627 ger DE-627 rakwb eng 510 ASE 31.49 bkl Zhang, Benxin verfasserin aut A primal-dual algorithm framework for convex saddle-point optimization 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In this study, we introduce a primal-dual prediction-correction algorithm framework for convex optimization problems with known saddle-point structure. Our unified frame adds the proximal term with a positive definite weighting matrix. Moreover, different proximal parameters in the frame can derive some existing well-known algorithms and yield a class of new primal-dual schemes. We prove the convergence of the proposed frame from the perspective of proximal point algorithm-like contraction methods and variational inequalities approach. The convergence rate $O(1/t)$ in the ergodic and nonergodic senses is also given, where t denotes the iteration number. primal-dual method (dpeaa)DE-He213 proximal point algorithm (dpeaa)DE-He213 convex optimization (dpeaa)DE-He213 variational inequalities (dpeaa)DE-He213 Zhu, Zhibin verfasserin aut Enthalten in Journal of inequalities and applications Heidelberg : Springer, 2005 2017(2017), 1 vom: 25. Okt. (DE-627)320977056 (DE-600)2028512-7 1029-242X nnns volume:2017 year:2017 number:1 day:25 month:10 https://dx.doi.org/10.1186/s13660-017-1548-z kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2027 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 31.49 ASE AR 2017 2017 1 25 10
allfieldsGer	10.1186/s13660-017-1548-z doi (DE-627)SPR032566255 (SPR)s13660-017-1548-z-e DE-627 ger DE-627 rakwb eng 510 ASE 31.49 bkl Zhang, Benxin verfasserin aut A primal-dual algorithm framework for convex saddle-point optimization 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In this study, we introduce a primal-dual prediction-correction algorithm framework for convex optimization problems with known saddle-point structure. Our unified frame adds the proximal term with a positive definite weighting matrix. Moreover, different proximal parameters in the frame can derive some existing well-known algorithms and yield a class of new primal-dual schemes. We prove the convergence of the proposed frame from the perspective of proximal point algorithm-like contraction methods and variational inequalities approach. The convergence rate $O(1/t)$ in the ergodic and nonergodic senses is also given, where t denotes the iteration number. primal-dual method (dpeaa)DE-He213 proximal point algorithm (dpeaa)DE-He213 convex optimization (dpeaa)DE-He213 variational inequalities (dpeaa)DE-He213 Zhu, Zhibin verfasserin aut Enthalten in Journal of inequalities and applications Heidelberg : Springer, 2005 2017(2017), 1 vom: 25. Okt. (DE-627)320977056 (DE-600)2028512-7 1029-242X nnns volume:2017 year:2017 number:1 day:25 month:10 https://dx.doi.org/10.1186/s13660-017-1548-z kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2027 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 31.49 ASE AR 2017 2017 1 25 10
allfieldsSound	10.1186/s13660-017-1548-z doi (DE-627)SPR032566255 (SPR)s13660-017-1548-z-e DE-627 ger DE-627 rakwb eng 510 ASE 31.49 bkl Zhang, Benxin verfasserin aut A primal-dual algorithm framework for convex saddle-point optimization 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In this study, we introduce a primal-dual prediction-correction algorithm framework for convex optimization problems with known saddle-point structure. Our unified frame adds the proximal term with a positive definite weighting matrix. Moreover, different proximal parameters in the frame can derive some existing well-known algorithms and yield a class of new primal-dual schemes. We prove the convergence of the proposed frame from the perspective of proximal point algorithm-like contraction methods and variational inequalities approach. The convergence rate $O(1/t)$ in the ergodic and nonergodic senses is also given, where t denotes the iteration number. primal-dual method (dpeaa)DE-He213 proximal point algorithm (dpeaa)DE-He213 convex optimization (dpeaa)DE-He213 variational inequalities (dpeaa)DE-He213 Zhu, Zhibin verfasserin aut Enthalten in Journal of inequalities and applications Heidelberg : Springer, 2005 2017(2017), 1 vom: 25. Okt. (DE-627)320977056 (DE-600)2028512-7 1029-242X nnns volume:2017 year:2017 number:1 day:25 month:10 https://dx.doi.org/10.1186/s13660-017-1548-z kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2027 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 31.49 ASE AR 2017 2017 1 25 10
language	English
source	Enthalten in Journal of inequalities and applications 2017(2017), 1 vom: 25. Okt. volume:2017 year:2017 number:1 day:25 month:10
sourceStr	Enthalten in Journal of inequalities and applications 2017(2017), 1 vom: 25. Okt. volume:2017 year:2017 number:1 day:25 month:10
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	primal-dual method proximal point algorithm convex optimization variational inequalities
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author	Zhang, Benxin
spellingShingle	Zhang, Benxin ddc 510 bkl 31.49 misc primal-dual method misc proximal point algorithm misc convex optimization misc variational inequalities A primal-dual algorithm framework for convex saddle-point optimization
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topic_title	510 ASE 31.49 bkl A primal-dual algorithm framework for convex saddle-point optimization primal-dual method (dpeaa)DE-He213 proximal point algorithm (dpeaa)DE-He213 convex optimization (dpeaa)DE-He213 variational inequalities (dpeaa)DE-He213
topic	ddc 510 bkl 31.49 misc primal-dual method misc proximal point algorithm misc convex optimization misc variational inequalities
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title	A primal-dual algorithm framework for convex saddle-point optimization
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title_full	A primal-dual algorithm framework for convex saddle-point optimization
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title_sort	primal-dual algorithm framework for convex saddle-point optimization
title_auth	A primal-dual algorithm framework for convex saddle-point optimization
abstract	Abstract In this study, we introduce a primal-dual prediction-correction algorithm framework for convex optimization problems with known saddle-point structure. Our unified frame adds the proximal term with a positive definite weighting matrix. Moreover, different proximal parameters in the frame can derive some existing well-known algorithms and yield a class of new primal-dual schemes. We prove the convergence of the proposed frame from the perspective of proximal point algorithm-like contraction methods and variational inequalities approach. The convergence rate $O(1/t)$ in the ergodic and nonergodic senses is also given, where t denotes the iteration number.
abstractGer	Abstract In this study, we introduce a primal-dual prediction-correction algorithm framework for convex optimization problems with known saddle-point structure. Our unified frame adds the proximal term with a positive definite weighting matrix. Moreover, different proximal parameters in the frame can derive some existing well-known algorithms and yield a class of new primal-dual schemes. We prove the convergence of the proposed frame from the perspective of proximal point algorithm-like contraction methods and variational inequalities approach. The convergence rate $O(1/t)$ in the ergodic and nonergodic senses is also given, where t denotes the iteration number.
abstract_unstemmed	Abstract In this study, we introduce a primal-dual prediction-correction algorithm framework for convex optimization problems with known saddle-point structure. Our unified frame adds the proximal term with a positive definite weighting matrix. Moreover, different proximal parameters in the frame can derive some existing well-known algorithms and yield a class of new primal-dual schemes. We prove the convergence of the proposed frame from the perspective of proximal point algorithm-like contraction methods and variational inequalities approach. The convergence rate $O(1/t)$ in the ergodic and nonergodic senses is also given, where t denotes the iteration number.
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title_short	A primal-dual algorithm framework for convex saddle-point optimization
url	https://dx.doi.org/10.1186/s13660-017-1548-z
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A primal-dual algorithm framework for convex saddle-point optimization

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