General viscosity iterative approximation for solving unconstrained convex optimization problems

Abstract In this paper, we combine a sequence of contractive mappings $\{h_{n}\}$ with the proximal operator and propose a generalized viscosity approximation method for solving the unconstrained convex optimization problems in a real Hilbert space H. We show that, under reasonable parameter conditi...
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Gespeichert in:

Autor*in:	Duan, Peichao [verfasserIn] Song, Miaomiao [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2015

Schlagwörter:	contractive mapping nonexpansive mapping proximal operator variational inequality problem

Übergeordnetes Werk:	Enthalten in: Journal of inequalities and applications - Heidelberg : Springer, 2005, 2015(2015), 1 vom: 16. Okt.
Übergeordnetes Werk:	volume:2015 ; year:2015 ; number:1 ; day:16 ; month:10

Links:	Volltext

DOI / URN:	10.1186/s13660-015-0857-3

Katalog-ID:	SPR032533217

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allfields	10.1186/s13660-015-0857-3 doi (DE-627)SPR032533217 (SPR)s13660-015-0857-3-e DE-627 ger DE-627 rakwb eng 510 ASE 31.49 bkl Duan, Peichao verfasserin aut General viscosity iterative approximation for solving unconstrained convex optimization problems 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In this paper, we combine a sequence of contractive mappings $\{h_{n}\}$ with the proximal operator and propose a generalized viscosity approximation method for solving the unconstrained convex optimization problems in a real Hilbert space H. We show that, under reasonable parameter conditions, our algorithm strongly converges to the unique solution of a variational inequality problem. Our result presented in the paper improves and extends the corresponding results reported by many authors recently. contractive mapping (dpeaa)DE-He213 nonexpansive mapping (dpeaa)DE-He213 proximal operator (dpeaa)DE-He213 variational inequality problem (dpeaa)DE-He213 Song, Miaomiao verfasserin aut Enthalten in Journal of inequalities and applications Heidelberg : Springer, 2005 2015(2015), 1 vom: 16. Okt. (DE-627)320977056 (DE-600)2028512-7 1029-242X nnns volume:2015 year:2015 number:1 day:16 month:10 https://dx.doi.org/10.1186/s13660-015-0857-3 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 2015 2015 1 16 10
spelling	10.1186/s13660-015-0857-3 doi (DE-627)SPR032533217 (SPR)s13660-015-0857-3-e DE-627 ger DE-627 rakwb eng 510 ASE 31.49 bkl Duan, Peichao verfasserin aut General viscosity iterative approximation for solving unconstrained convex optimization problems 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In this paper, we combine a sequence of contractive mappings $\{h_{n}\}$ with the proximal operator and propose a generalized viscosity approximation method for solving the unconstrained convex optimization problems in a real Hilbert space H. We show that, under reasonable parameter conditions, our algorithm strongly converges to the unique solution of a variational inequality problem. Our result presented in the paper improves and extends the corresponding results reported by many authors recently. contractive mapping (dpeaa)DE-He213 nonexpansive mapping (dpeaa)DE-He213 proximal operator (dpeaa)DE-He213 variational inequality problem (dpeaa)DE-He213 Song, Miaomiao verfasserin aut Enthalten in Journal of inequalities and applications Heidelberg : Springer, 2005 2015(2015), 1 vom: 16. Okt. (DE-627)320977056 (DE-600)2028512-7 1029-242X nnns volume:2015 year:2015 number:1 day:16 month:10 https://dx.doi.org/10.1186/s13660-015-0857-3 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 2015 2015 1 16 10
allfields_unstemmed	10.1186/s13660-015-0857-3 doi (DE-627)SPR032533217 (SPR)s13660-015-0857-3-e DE-627 ger DE-627 rakwb eng 510 ASE 31.49 bkl Duan, Peichao verfasserin aut General viscosity iterative approximation for solving unconstrained convex optimization problems 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In this paper, we combine a sequence of contractive mappings $\{h_{n}\}$ with the proximal operator and propose a generalized viscosity approximation method for solving the unconstrained convex optimization problems in a real Hilbert space H. We show that, under reasonable parameter conditions, our algorithm strongly converges to the unique solution of a variational inequality problem. Our result presented in the paper improves and extends the corresponding results reported by many authors recently. contractive mapping (dpeaa)DE-He213 nonexpansive mapping (dpeaa)DE-He213 proximal operator (dpeaa)DE-He213 variational inequality problem (dpeaa)DE-He213 Song, Miaomiao verfasserin aut Enthalten in Journal of inequalities and applications Heidelberg : Springer, 2005 2015(2015), 1 vom: 16. Okt. (DE-627)320977056 (DE-600)2028512-7 1029-242X nnns volume:2015 year:2015 number:1 day:16 month:10 https://dx.doi.org/10.1186/s13660-015-0857-3 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 2015 2015 1 16 10
allfieldsGer	10.1186/s13660-015-0857-3 doi (DE-627)SPR032533217 (SPR)s13660-015-0857-3-e DE-627 ger DE-627 rakwb eng 510 ASE 31.49 bkl Duan, Peichao verfasserin aut General viscosity iterative approximation for solving unconstrained convex optimization problems 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In this paper, we combine a sequence of contractive mappings $\{h_{n}\}$ with the proximal operator and propose a generalized viscosity approximation method for solving the unconstrained convex optimization problems in a real Hilbert space H. We show that, under reasonable parameter conditions, our algorithm strongly converges to the unique solution of a variational inequality problem. Our result presented in the paper improves and extends the corresponding results reported by many authors recently. contractive mapping (dpeaa)DE-He213 nonexpansive mapping (dpeaa)DE-He213 proximal operator (dpeaa)DE-He213 variational inequality problem (dpeaa)DE-He213 Song, Miaomiao verfasserin aut Enthalten in Journal of inequalities and applications Heidelberg : Springer, 2005 2015(2015), 1 vom: 16. Okt. (DE-627)320977056 (DE-600)2028512-7 1029-242X nnns volume:2015 year:2015 number:1 day:16 month:10 https://dx.doi.org/10.1186/s13660-015-0857-3 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 2015 2015 1 16 10
allfieldsSound	10.1186/s13660-015-0857-3 doi (DE-627)SPR032533217 (SPR)s13660-015-0857-3-e DE-627 ger DE-627 rakwb eng 510 ASE 31.49 bkl Duan, Peichao verfasserin aut General viscosity iterative approximation for solving unconstrained convex optimization problems 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In this paper, we combine a sequence of contractive mappings $\{h_{n}\}$ with the proximal operator and propose a generalized viscosity approximation method for solving the unconstrained convex optimization problems in a real Hilbert space H. We show that, under reasonable parameter conditions, our algorithm strongly converges to the unique solution of a variational inequality problem. Our result presented in the paper improves and extends the corresponding results reported by many authors recently. contractive mapping (dpeaa)DE-He213 nonexpansive mapping (dpeaa)DE-He213 proximal operator (dpeaa)DE-He213 variational inequality problem (dpeaa)DE-He213 Song, Miaomiao verfasserin aut Enthalten in Journal of inequalities and applications Heidelberg : Springer, 2005 2015(2015), 1 vom: 16. Okt. (DE-627)320977056 (DE-600)2028512-7 1029-242X nnns volume:2015 year:2015 number:1 day:16 month:10 https://dx.doi.org/10.1186/s13660-015-0857-3 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 2015 2015 1 16 10
language	English
source	Enthalten in Journal of inequalities and applications 2015(2015), 1 vom: 16. Okt. volume:2015 year:2015 number:1 day:16 month:10
sourceStr	Enthalten in Journal of inequalities and applications 2015(2015), 1 vom: 16. Okt. volume:2015 year:2015 number:1 day:16 month:10
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	contractive mapping nonexpansive mapping proximal operator variational inequality problem
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container_title	Journal of inequalities and applications
authorswithroles_txt_mv	Duan, Peichao @@aut@@ Song, Miaomiao @@aut@@
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author	Duan, Peichao
spellingShingle	Duan, Peichao ddc 510 bkl 31.49 misc contractive mapping misc nonexpansive mapping misc proximal operator misc variational inequality problem General viscosity iterative approximation for solving unconstrained convex optimization problems
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topic_title	510 ASE 31.49 bkl General viscosity iterative approximation for solving unconstrained convex optimization problems contractive mapping (dpeaa)DE-He213 nonexpansive mapping (dpeaa)DE-He213 proximal operator (dpeaa)DE-He213 variational inequality problem (dpeaa)DE-He213
topic	ddc 510 bkl 31.49 misc contractive mapping misc nonexpansive mapping misc proximal operator misc variational inequality problem
topic_unstemmed	ddc 510 bkl 31.49 misc contractive mapping misc nonexpansive mapping misc proximal operator misc variational inequality problem
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title	General viscosity iterative approximation for solving unconstrained convex optimization problems
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title_full	General viscosity iterative approximation for solving unconstrained convex optimization problems
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title_sort	general viscosity iterative approximation for solving unconstrained convex optimization problems
title_auth	General viscosity iterative approximation for solving unconstrained convex optimization problems
abstract	Abstract In this paper, we combine a sequence of contractive mappings $\{h_{n}\}$ with the proximal operator and propose a generalized viscosity approximation method for solving the unconstrained convex optimization problems in a real Hilbert space H. We show that, under reasonable parameter conditions, our algorithm strongly converges to the unique solution of a variational inequality problem. Our result presented in the paper improves and extends the corresponding results reported by many authors recently.
abstractGer	Abstract In this paper, we combine a sequence of contractive mappings $\{h_{n}\}$ with the proximal operator and propose a generalized viscosity approximation method for solving the unconstrained convex optimization problems in a real Hilbert space H. We show that, under reasonable parameter conditions, our algorithm strongly converges to the unique solution of a variational inequality problem. Our result presented in the paper improves and extends the corresponding results reported by many authors recently.
abstract_unstemmed	Abstract In this paper, we combine a sequence of contractive mappings $\{h_{n}\}$ with the proximal operator and propose a generalized viscosity approximation method for solving the unconstrained convex optimization problems in a real Hilbert space H. We show that, under reasonable parameter conditions, our algorithm strongly converges to the unique solution of a variational inequality problem. Our result presented in the paper improves and extends the corresponding results reported by many authors recently.
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title_short	General viscosity iterative approximation for solving unconstrained convex optimization problems
url	https://dx.doi.org/10.1186/s13660-015-0857-3
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up_date	2024-07-03T13:24:34.791Z
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