Parallel extragradient algorithms for multiple set split equilibrium problems in Hilbert spaces
In this paper, we introduce an extension of multiple set split variational inequality problem (Censor et al. Numer. Algor. 59 , 301–323 2012 ) to multiple set split equilibrium problem (MSSEP) and propose two new parallel extragradient algorithms for solving MSSEP when the equilibrium bifunctions ar...
Gespeichert in:
| Veröffentlicht in: | Numerical algorithms 2018-03, Vol.77 (3), p.741-761 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 761 |
|---|---|
| container_issue | 3 |
| container_start_page | 741 |
| container_title | Numerical algorithms |
| container_volume | 77 |
| creator | Kim, Do Sang Van Dinh, Bui |
| description | In this paper, we introduce an extension of multiple set split variational inequality problem (Censor et al. Numer. Algor.
59
, 301–323
2012
) to multiple set split equilibrium problem (MSSEP) and propose two new parallel extragradient algorithms for solving MSSEP when the equilibrium bifunctions are Lipschitz-type continuous and pseudo-monotone with respect to their solution sets. By using extragradient method combining with cutting techniques, we obtain algorithms for these problems without using any product space. Under certain conditions on parameters, the iteration sequences generated by the proposed algorithms are proved to be weakly and strongly convergent to a solution of MSSEP. An application to multiple set split variational inequality problems and a numerical example and preliminary computational results are also provided. |
| doi_str_mv | 10.1007/s11075-017-0338-5 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2918586931</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2918586931</sourcerecordid><originalsourceid>FETCH-LOGICAL-c316t-abf3e7952f5d758aeb0449d01097f5860b9010c308623e2f51b904221c7abb8f3</originalsourceid><addsrcrecordid>eNp1kE1LAzEQhoMoWKs_wFvA82o-ms3mKEVtoaAHPYdkO1tTsh9NsqD_3iwrePI0w8zzvjO8CN1Sck8JkQ-RUiJFQagsCOdVIc7QggrJCsVKcZ77aUO5qi7RVYxHQrKKyQXSbyYY78Fj-ErBHILZO-gSNv7QB5c-24ibPuB29MkNHnCEhOPgXcJwGp13NrixxUPorYfMug5vnLcQJsrUEK_RRWN8hJvfukQfz0_v602xe33Zrh93Rc1pmQpjGw5SCdaIvRSVAUtWK7XPXyrZiKokVuW-5qQqGYdM0TxYMUZraaytGr5Ed7NvfuU0Qkz62I-hyyc1U7TKForTTNGZqkMfY4BGD8G1JnxrSvSUo55z1DktPeWoRdawWRMz2x0g_Dn_L_oBwfp2Vw</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2918586931</pqid></control><display><type>article</type><title>Parallel extragradient algorithms for multiple set split equilibrium problems in Hilbert spaces</title><source>SpringerLink Journals</source><creator>Kim, Do Sang ; Van Dinh, Bui</creator><creatorcontrib>Kim, Do Sang ; Van Dinh, Bui</creatorcontrib><description>In this paper, we introduce an extension of multiple set split variational inequality problem (Censor et al. Numer. Algor.
59
, 301–323
2012
) to multiple set split equilibrium problem (MSSEP) and propose two new parallel extragradient algorithms for solving MSSEP when the equilibrium bifunctions are Lipschitz-type continuous and pseudo-monotone with respect to their solution sets. By using extragradient method combining with cutting techniques, we obtain algorithms for these problems without using any product space. Under certain conditions on parameters, the iteration sequences generated by the proposed algorithms are proved to be weakly and strongly convergent to a solution of MSSEP. An application to multiple set split variational inequality problems and a numerical example and preliminary computational results are also provided.</description><identifier>ISSN: 1017-1398</identifier><identifier>EISSN: 1572-9265</identifier><identifier>DOI: 10.1007/s11075-017-0338-5</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Algebra ; Algorithms ; Computer Science ; Data compression ; Equilibrium ; Hilbert space ; Iterative methods ; Methods ; Numeric Computing ; Numerical Analysis ; Original Paper ; Theory of Computation</subject><ispartof>Numerical algorithms, 2018-03, Vol.77 (3), p.741-761</ispartof><rights>Springer Science+Business Media New York 2017</rights><rights>Springer Science+Business Media New York 2017.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c316t-abf3e7952f5d758aeb0449d01097f5860b9010c308623e2f51b904221c7abb8f3</citedby><cites>FETCH-LOGICAL-c316t-abf3e7952f5d758aeb0449d01097f5860b9010c308623e2f51b904221c7abb8f3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s11075-017-0338-5$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s11075-017-0338-5$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27901,27902,41464,42533,51294</link.rule.ids></links><search><creatorcontrib>Kim, Do Sang</creatorcontrib><creatorcontrib>Van Dinh, Bui</creatorcontrib><title>Parallel extragradient algorithms for multiple set split equilibrium problems in Hilbert spaces</title><title>Numerical algorithms</title><addtitle>Numer Algor</addtitle><description>In this paper, we introduce an extension of multiple set split variational inequality problem (Censor et al. Numer. Algor.
59
, 301–323
2012
) to multiple set split equilibrium problem (MSSEP) and propose two new parallel extragradient algorithms for solving MSSEP when the equilibrium bifunctions are Lipschitz-type continuous and pseudo-monotone with respect to their solution sets. By using extragradient method combining with cutting techniques, we obtain algorithms for these problems without using any product space. Under certain conditions on parameters, the iteration sequences generated by the proposed algorithms are proved to be weakly and strongly convergent to a solution of MSSEP. An application to multiple set split variational inequality problems and a numerical example and preliminary computational results are also provided.</description><subject>Algebra</subject><subject>Algorithms</subject><subject>Computer Science</subject><subject>Data compression</subject><subject>Equilibrium</subject><subject>Hilbert space</subject><subject>Iterative methods</subject><subject>Methods</subject><subject>Numeric Computing</subject><subject>Numerical Analysis</subject><subject>Original Paper</subject><subject>Theory of Computation</subject><issn>1017-1398</issn><issn>1572-9265</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2018</creationdate><recordtype>article</recordtype><sourceid>BENPR</sourceid><recordid>eNp1kE1LAzEQhoMoWKs_wFvA82o-ms3mKEVtoaAHPYdkO1tTsh9NsqD_3iwrePI0w8zzvjO8CN1Sck8JkQ-RUiJFQagsCOdVIc7QggrJCsVKcZ77aUO5qi7RVYxHQrKKyQXSbyYY78Fj-ErBHILZO-gSNv7QB5c-24ibPuB29MkNHnCEhOPgXcJwGp13NrixxUPorYfMug5vnLcQJsrUEK_RRWN8hJvfukQfz0_v602xe33Zrh93Rc1pmQpjGw5SCdaIvRSVAUtWK7XPXyrZiKokVuW-5qQqGYdM0TxYMUZraaytGr5Ed7NvfuU0Qkz62I-hyyc1U7TKForTTNGZqkMfY4BGD8G1JnxrSvSUo55z1DktPeWoRdawWRMz2x0g_Dn_L_oBwfp2Vw</recordid><startdate>20180301</startdate><enddate>20180301</enddate><creator>Kim, Do Sang</creator><creator>Van Dinh, Bui</creator><general>Springer US</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>GNUQQ</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K7-</scope><scope>L6V</scope><scope>M7S</scope><scope>P62</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PTHSS</scope></search><sort><creationdate>20180301</creationdate><title>Parallel extragradient algorithms for multiple set split equilibrium problems in Hilbert spaces</title><author>Kim, Do Sang ; Van Dinh, Bui</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c316t-abf3e7952f5d758aeb0449d01097f5860b9010c308623e2f51b904221c7abb8f3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2018</creationdate><topic>Algebra</topic><topic>Algorithms</topic><topic>Computer Science</topic><topic>Data compression</topic><topic>Equilibrium</topic><topic>Hilbert space</topic><topic>Iterative methods</topic><topic>Methods</topic><topic>Numeric Computing</topic><topic>Numerical Analysis</topic><topic>Original Paper</topic><topic>Theory of Computation</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Kim, Do Sang</creatorcontrib><creatorcontrib>Van Dinh, Bui</creatorcontrib><collection>CrossRef</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central UK/Ireland</collection><collection>Advanced Technologies & Aerospace Collection</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>ProQuest Central Student</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Computer Science Collection</collection><collection>Computer Science Database</collection><collection>ProQuest Engineering Collection</collection><collection>Engineering Database</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>Engineering Collection</collection><jtitle>Numerical algorithms</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Kim, Do Sang</au><au>Van Dinh, Bui</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Parallel extragradient algorithms for multiple set split equilibrium problems in Hilbert spaces</atitle><jtitle>Numerical algorithms</jtitle><stitle>Numer Algor</stitle><date>2018-03-01</date><risdate>2018</risdate><volume>77</volume><issue>3</issue><spage>741</spage><epage>761</epage><pages>741-761</pages><issn>1017-1398</issn><eissn>1572-9265</eissn><abstract>In this paper, we introduce an extension of multiple set split variational inequality problem (Censor et al. Numer. Algor.
59
, 301–323
2012
) to multiple set split equilibrium problem (MSSEP) and propose two new parallel extragradient algorithms for solving MSSEP when the equilibrium bifunctions are Lipschitz-type continuous and pseudo-monotone with respect to their solution sets. By using extragradient method combining with cutting techniques, we obtain algorithms for these problems without using any product space. Under certain conditions on parameters, the iteration sequences generated by the proposed algorithms are proved to be weakly and strongly convergent to a solution of MSSEP. An application to multiple set split variational inequality problems and a numerical example and preliminary computational results are also provided.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s11075-017-0338-5</doi><tpages>21</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 1017-1398 |
| ispartof | Numerical algorithms, 2018-03, Vol.77 (3), p.741-761 |
| issn | 1017-1398 1572-9265 |
| language | eng |
| recordid | cdi_proquest_journals_2918586931 |
| source | SpringerLink Journals |
| subjects | Algebra Algorithms Computer Science Data compression Equilibrium Hilbert space Iterative methods Methods Numeric Computing Numerical Analysis Original Paper Theory of Computation |
| title | Parallel extragradient algorithms for multiple set split equilibrium problems in Hilbert spaces |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-02-13T05%3A52%3A23IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Parallel%20extragradient%20algorithms%20for%20multiple%20set%20split%20equilibrium%20problems%20in%20Hilbert%20spaces&rft.jtitle=Numerical%20algorithms&rft.au=Kim,%20Do%20Sang&rft.date=2018-03-01&rft.volume=77&rft.issue=3&rft.spage=741&rft.epage=761&rft.pages=741-761&rft.issn=1017-1398&rft.eissn=1572-9265&rft_id=info:doi/10.1007/s11075-017-0338-5&rft_dat=%3Cproquest_cross%3E2918586931%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2918586931&rft_id=info:pmid/&rfr_iscdi=true |