On the solution stability of variational inequalities
In the present paper, we will study the solution stability of parametric variational conditions 0 f (, x) + NK()(x), where M and are topological spaces, f : M Rn Rn is a function, K : 2Rn is a multifunction and NK()(x) is the value at x of the normal cone operator associated with the set K(). By usi...
Gespeichert in:
| Veröffentlicht in: | Journal of global optimization 2007-09, Vol.39 (1), p.101-111 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 111 |
|---|---|
| container_issue | 1 |
| container_start_page | 101 |
| container_title | Journal of global optimization |
| container_volume | 39 |
| creator | Kien, B. T. Wong, M. -M. |
| description | In the present paper, we will study the solution stability of parametric variational conditions 0 f (, x) + NK()(x), where M and are topological spaces, f : M Rn Rn is a function, K : 2Rn is a multifunction and NK()(x) is the value at x of the normal cone operator associated with the set K(). By using the degree theory and the natural map we show that under certain conditions, the solution map of the problem is lower semicontinuous with respect to parameters (, ). Our results are different versions of Robinsons results [15] and proved directly without the homeomorphic result between the solution sets. [PUBLICATION ABSTRACT] |
| doi_str_mv | 10.1007/s10898-006-9125-x |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_194676547</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>1311073301</sourcerecordid><originalsourceid>FETCH-LOGICAL-c272t-ef1a4cf694b0d6aa4a48898a8b74467c315a0a2453770641dd61e1973098be93</originalsourceid><addsrcrecordid>eNotkMtqwzAQRUVpoW7aD-jOdK92xtbDWpbQFwSyyV6MbZkquHYi2SX5-8qkq4E7l8vhMPaI8IwA-iUiVKbiAIobLCQ_XbEMpS55YVBdswxMCiUA3rK7GPcAYCpZZExuh3z6dnkc-3ny45DHiWrf--mcj13-S8HTElOf-8EdZ0of7-I9u-moj-7h_67Y7v1tt_7km-3H1_p1w5tCFxN3HZJoOmVEDa0iEiSqRElVrYVQuilRElAhZKk1KIFtq9Ch0WWCq50pV-zpMnsI43F2cbL7cQ4JJlo0aUBJoVMJL6UmjDEG19lD8D8UzhbBLm7sxY1Nbuzixp7KP3fjVpo</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>194676547</pqid></control><display><type>article</type><title>On the solution stability of variational inequalities</title><source>SpringerLink Journals - AutoHoldings</source><creator>Kien, B. T. ; Wong, M. -M.</creator><creatorcontrib>Kien, B. T. ; Wong, M. -M.</creatorcontrib><description>In the present paper, we will study the solution stability of parametric variational conditions 0 f (, x) + NK()(x), where M and are topological spaces, f : M Rn Rn is a function, K : 2Rn is a multifunction and NK()(x) is the value at x of the normal cone operator associated with the set K(). By using the degree theory and the natural map we show that under certain conditions, the solution map of the problem is lower semicontinuous with respect to parameters (, ). Our results are different versions of Robinsons results [15] and proved directly without the homeomorphic result between the solution sets. [PUBLICATION ABSTRACT]</description><identifier>ISSN: 0925-5001</identifier><identifier>EISSN: 1573-2916</identifier><identifier>DOI: 10.1007/s10898-006-9125-x</identifier><language>eng</language><publisher>Dordrecht: Springer Nature B.V</publisher><subject>Localization ; Mathematical models ; Neighborhoods ; Optimization ; Studies</subject><ispartof>Journal of global optimization, 2007-09, Vol.39 (1), p.101-111</ispartof><rights>Springer Science+Business Media LLC 2007</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c272t-ef1a4cf694b0d6aa4a48898a8b74467c315a0a2453770641dd61e1973098be93</citedby><cites>FETCH-LOGICAL-c272t-ef1a4cf694b0d6aa4a48898a8b74467c315a0a2453770641dd61e1973098be93</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27924,27925</link.rule.ids></links><search><creatorcontrib>Kien, B. T.</creatorcontrib><creatorcontrib>Wong, M. -M.</creatorcontrib><title>On the solution stability of variational inequalities</title><title>Journal of global optimization</title><description>In the present paper, we will study the solution stability of parametric variational conditions 0 f (, x) + NK()(x), where M and are topological spaces, f : M Rn Rn is a function, K : 2Rn is a multifunction and NK()(x) is the value at x of the normal cone operator associated with the set K(). By using the degree theory and the natural map we show that under certain conditions, the solution map of the problem is lower semicontinuous with respect to parameters (, ). Our results are different versions of Robinsons results [15] and proved directly without the homeomorphic result between the solution sets. [PUBLICATION ABSTRACT]</description><subject>Localization</subject><subject>Mathematical models</subject><subject>Neighborhoods</subject><subject>Optimization</subject><subject>Studies</subject><issn>0925-5001</issn><issn>1573-2916</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2007</creationdate><recordtype>article</recordtype><sourceid>8G5</sourceid><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GNUQQ</sourceid><sourceid>GUQSH</sourceid><sourceid>M2O</sourceid><recordid>eNotkMtqwzAQRUVpoW7aD-jOdK92xtbDWpbQFwSyyV6MbZkquHYi2SX5-8qkq4E7l8vhMPaI8IwA-iUiVKbiAIobLCQ_XbEMpS55YVBdswxMCiUA3rK7GPcAYCpZZExuh3z6dnkc-3ny45DHiWrf--mcj13-S8HTElOf-8EdZ0of7-I9u-moj-7h_67Y7v1tt_7km-3H1_p1w5tCFxN3HZJoOmVEDa0iEiSqRElVrYVQuilRElAhZKk1KIFtq9Ch0WWCq50pV-zpMnsI43F2cbL7cQ4JJlo0aUBJoVMJL6UmjDEG19lD8D8UzhbBLm7sxY1Nbuzixp7KP3fjVpo</recordid><startdate>20070901</startdate><enddate>20070901</enddate><creator>Kien, B. T.</creator><creator>Wong, M. -M.</creator><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>0U~</scope><scope>1-H</scope><scope>3V.</scope><scope>7SC</scope><scope>7WY</scope><scope>7WZ</scope><scope>7XB</scope><scope>87Z</scope><scope>88I</scope><scope>8AL</scope><scope>8AO</scope><scope>8FD</scope><scope>8FE</scope><scope>8FG</scope><scope>8FK</scope><scope>8FL</scope><scope>8G5</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BEZIV</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>FRNLG</scope><scope>F~G</scope><scope>GNUQQ</scope><scope>GUQSH</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K60</scope><scope>K6~</scope><scope>K7-</scope><scope>L.-</scope><scope>L.0</scope><scope>L6V</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>M0C</scope><scope>M0N</scope><scope>M2O</scope><scope>M2P</scope><scope>M7S</scope><scope>MBDVC</scope><scope>P5Z</scope><scope>P62</scope><scope>PQBIZ</scope><scope>PQBZA</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PTHSS</scope><scope>Q9U</scope></search><sort><creationdate>20070901</creationdate><title>On the solution stability of variational inequalities</title><author>Kien, B. T. ; Wong, M. -M.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c272t-ef1a4cf694b0d6aa4a48898a8b74467c315a0a2453770641dd61e1973098be93</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2007</creationdate><topic>Localization</topic><topic>Mathematical models</topic><topic>Neighborhoods</topic><topic>Optimization</topic><topic>Studies</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Kien, B. T.</creatorcontrib><creatorcontrib>Wong, M. -M.</creatorcontrib><collection>CrossRef</collection><collection>Global News & ABI/Inform Professional</collection><collection>Trade PRO</collection><collection>ProQuest Central (Corporate)</collection><collection>Computer and Information Systems Abstracts</collection><collection>Access via ABI/INFORM (ProQuest)</collection><collection>ABI/INFORM Global (PDF only)</collection><collection>ProQuest Central (purchase pre-March 2016)</collection><collection>ABI/INFORM Global (Alumni Edition)</collection><collection>Science Database (Alumni Edition)</collection><collection>Computing Database (Alumni Edition)</collection><collection>ProQuest Pharma Collection</collection><collection>Technology Research Database</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Central (Alumni) (purchase pre-March 2016)</collection><collection>ABI/INFORM Collection (Alumni Edition)</collection><collection>Research Library (Alumni Edition)</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>Advanced Technologies & Aerospace Collection</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Business Premium Collection</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>Business Premium Collection (Alumni)</collection><collection>ABI/INFORM Global (Corporate)</collection><collection>ProQuest Central Student</collection><collection>Research Library Prep</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Computer Science Collection</collection><collection>ProQuest Business Collection (Alumni Edition)</collection><collection>ProQuest Business Collection</collection><collection>Computer Science Database</collection><collection>ABI/INFORM Professional Advanced</collection><collection>ABI/INFORM Professional Standard</collection><collection>ProQuest Engineering Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><collection>ABI/INFORM Global</collection><collection>Computing Database</collection><collection>Research Library</collection><collection>Science Database</collection><collection>Engineering Database</collection><collection>Research Library (Corporate)</collection><collection>Advanced Technologies & Aerospace Database</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>ProQuest One Business</collection><collection>ProQuest One Business (Alumni)</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><collection>ProQuest Central Basic</collection><jtitle>Journal of global optimization</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Kien, B. T.</au><au>Wong, M. -M.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On the solution stability of variational inequalities</atitle><jtitle>Journal of global optimization</jtitle><date>2007-09-01</date><risdate>2007</risdate><volume>39</volume><issue>1</issue><spage>101</spage><epage>111</epage><pages>101-111</pages><issn>0925-5001</issn><eissn>1573-2916</eissn><abstract>In the present paper, we will study the solution stability of parametric variational conditions 0 f (, x) + NK()(x), where M and are topological spaces, f : M Rn Rn is a function, K : 2Rn is a multifunction and NK()(x) is the value at x of the normal cone operator associated with the set K(). By using the degree theory and the natural map we show that under certain conditions, the solution map of the problem is lower semicontinuous with respect to parameters (, ). Our results are different versions of Robinsons results [15] and proved directly without the homeomorphic result between the solution sets. [PUBLICATION ABSTRACT]</abstract><cop>Dordrecht</cop><pub>Springer Nature B.V</pub><doi>10.1007/s10898-006-9125-x</doi><tpages>11</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0925-5001 |
| ispartof | Journal of global optimization, 2007-09, Vol.39 (1), p.101-111 |
| issn | 0925-5001 1573-2916 |
| language | eng |
| recordid | cdi_proquest_journals_194676547 |
| source | SpringerLink Journals - AutoHoldings |
| subjects | Localization Mathematical models Neighborhoods Optimization Studies |
| title | On the solution stability of variational inequalities |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-03T10%3A05%3A31IST&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=On%20the%20solution%20stability%20of%20variational%20inequalities&rft.jtitle=Journal%20of%20global%20optimization&rft.au=Kien,%20B.%20T.&rft.date=2007-09-01&rft.volume=39&rft.issue=1&rft.spage=101&rft.epage=111&rft.pages=101-111&rft.issn=0925-5001&rft.eissn=1573-2916&rft_id=info:doi/10.1007/s10898-006-9125-x&rft_dat=%3Cproquest_cross%3E1311073301%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=194676547&rft_id=info:pmid/&rfr_iscdi=true |