Smoothing Newton method for NCP with the identification of degenerate indices
We present a new smoothing Newton method for nonlinear complementarity problems (NCP(F)) by using an NCP function to reformulate the problem to its equivalent form. Compared with most current smoothing methods, our method contains an estimating technique based on the active-set strategy. This techni...
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| Veröffentlicht in: | Journal of computational and applied mathematics 2010-10, Vol.234 (12), p.3424-3435 |
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| container_end_page | 3435 |
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| container_issue | 12 |
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| container_title | Journal of computational and applied mathematics |
| container_volume | 234 |
| creator | Yu, Haodong Pu, Dingguo |
| description | We present a new smoothing Newton method for nonlinear complementarity problems (NCP(F)) by using an NCP function to reformulate the problem to its equivalent form. Compared with most current smoothing methods, our method contains an estimating technique based on the active-set strategy. This technique focuses on the identification of the degenerate set for a solution
x
∗
of the NCP(F). The proposed method has the global convergence, each accumulation point is a solution of the problem. The introduction of the active-set strategy effectively reduces the scale of the problem. Under some regularity assumption, the degenerate set can be identified correctly near the solution and local superlinear convergence is obtained as well. |
| doi_str_mv | 10.1016/j.cam.2010.05.004 |
| format | Article |
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x
∗
of the NCP(F). The proposed method has the global convergence, each accumulation point is a solution of the problem. The introduction of the active-set strategy effectively reduces the scale of the problem. Under some regularity assumption, the degenerate set can be identified correctly near the solution and local superlinear convergence is obtained as well.</description><identifier>ISSN: 0377-0427</identifier><identifier>EISSN: 1879-1778</identifier><identifier>DOI: 10.1016/j.cam.2010.05.004</identifier><identifier>CODEN: JCAMDI</identifier><language>eng</language><publisher>Kidlington: Elsevier B.V</publisher><subject>Convergence ; Degenerate indices ; Equivalence ; Exact sciences and technology ; Global analysis, analysis on manifolds ; Global convergence ; Mathematical analysis ; Mathematical models ; Mathematics ; Newton methods ; Nonlinear algebraic and transcendental equations ; Nonlinear complementarity problems ; Nonlinearity ; Numerical analysis ; Numerical analysis. Scientific computation ; Regularity ; Sciences and techniques of general use ; Smoothing ; Smoothing methods ; Strategy ; Superlinear convergence ; Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds</subject><ispartof>Journal of computational and applied mathematics, 2010-10, Vol.234 (12), p.3424-3435</ispartof><rights>2010 Elsevier B.V.</rights><rights>2015 INIST-CNRS</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c402t-77b362466b75578021f3dbe638ed9b3d592517e6a52ca25d63839eb8cdd679353</citedby><cites>FETCH-LOGICAL-c402t-77b362466b75578021f3dbe638ed9b3d592517e6a52ca25d63839eb8cdd679353</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://dx.doi.org/10.1016/j.cam.2010.05.004$$EHTML$$P50$$Gelsevier$$Hfree_for_read</linktohtml><link.rule.ids>314,777,781,3537,27905,27906,45976</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=23072501$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Yu, Haodong</creatorcontrib><creatorcontrib>Pu, Dingguo</creatorcontrib><title>Smoothing Newton method for NCP with the identification of degenerate indices</title><title>Journal of computational and applied mathematics</title><description>We present a new smoothing Newton method for nonlinear complementarity problems (NCP(F)) by using an NCP function to reformulate the problem to its equivalent form. Compared with most current smoothing methods, our method contains an estimating technique based on the active-set strategy. This technique focuses on the identification of the degenerate set for a solution
x
∗
of the NCP(F). The proposed method has the global convergence, each accumulation point is a solution of the problem. The introduction of the active-set strategy effectively reduces the scale of the problem. Under some regularity assumption, the degenerate set can be identified correctly near the solution and local superlinear convergence is obtained as well.</description><subject>Convergence</subject><subject>Degenerate indices</subject><subject>Equivalence</subject><subject>Exact sciences and technology</subject><subject>Global analysis, analysis on manifolds</subject><subject>Global convergence</subject><subject>Mathematical analysis</subject><subject>Mathematical models</subject><subject>Mathematics</subject><subject>Newton methods</subject><subject>Nonlinear algebraic and transcendental equations</subject><subject>Nonlinear complementarity problems</subject><subject>Nonlinearity</subject><subject>Numerical analysis</subject><subject>Numerical analysis. Scientific computation</subject><subject>Regularity</subject><subject>Sciences and techniques of general use</subject><subject>Smoothing</subject><subject>Smoothing methods</subject><subject>Strategy</subject><subject>Superlinear convergence</subject><subject>Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds</subject><issn>0377-0427</issn><issn>1879-1778</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2010</creationdate><recordtype>article</recordtype><recordid>eNp9kM1rGzEQxUVJoI7TP6C3vYScdjuSVtIuOQXTL8gXJD0LrTQby3hXriQn9L-vjE2PPQ3D-703zCPkM4WGApVfNo01U8Og7CAagPYDWdBO9TVVqjsjC-BK1dAy9ZFcpLQBANnTdkHun6cQ8trPr9UDvucwVxPmdXDVGGL1sHqq3n1eV3mNlXc4Zz96a7IvWBgrh684YzS5iLPzFtMlOR_NNuGn01ySX9--vqx-1HeP33-ubu9q2wLLtVIDl6yVclBCqA4YHbkbUPIOXT9wJ3omqEJpBLOGCVcE3uPQWeek6rngS3J9zN3F8HuPKevJJ4vbrZkx7JNWEhhILvtC0iNpY0gp4qh30U8m_tEU9KE5vdGlOX1oToPQpbniuTqlm2TNdoxmtj79MzIOigmghbs5clheffMYdbIeZ4vOR7RZu-D_c-UvK8KCMQ</recordid><startdate>20101015</startdate><enddate>20101015</enddate><creator>Yu, Haodong</creator><creator>Pu, Dingguo</creator><general>Elsevier B.V</general><general>Elsevier</general><scope>6I.</scope><scope>AAFTH</scope><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>20101015</creationdate><title>Smoothing Newton method for NCP with the identification of degenerate indices</title><author>Yu, Haodong ; Pu, Dingguo</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c402t-77b362466b75578021f3dbe638ed9b3d592517e6a52ca25d63839eb8cdd679353</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2010</creationdate><topic>Convergence</topic><topic>Degenerate indices</topic><topic>Equivalence</topic><topic>Exact sciences and technology</topic><topic>Global analysis, analysis on manifolds</topic><topic>Global convergence</topic><topic>Mathematical analysis</topic><topic>Mathematical models</topic><topic>Mathematics</topic><topic>Newton methods</topic><topic>Nonlinear algebraic and transcendental equations</topic><topic>Nonlinear complementarity problems</topic><topic>Nonlinearity</topic><topic>Numerical analysis</topic><topic>Numerical analysis. Scientific computation</topic><topic>Regularity</topic><topic>Sciences and techniques of general use</topic><topic>Smoothing</topic><topic>Smoothing methods</topic><topic>Strategy</topic><topic>Superlinear convergence</topic><topic>Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Yu, Haodong</creatorcontrib><creatorcontrib>Pu, Dingguo</creatorcontrib><collection>ScienceDirect Open Access Titles</collection><collection>Elsevier:ScienceDirect:Open Access</collection><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Journal of computational and applied mathematics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Yu, Haodong</au><au>Pu, Dingguo</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Smoothing Newton method for NCP with the identification of degenerate indices</atitle><jtitle>Journal of computational and applied mathematics</jtitle><date>2010-10-15</date><risdate>2010</risdate><volume>234</volume><issue>12</issue><spage>3424</spage><epage>3435</epage><pages>3424-3435</pages><issn>0377-0427</issn><eissn>1879-1778</eissn><coden>JCAMDI</coden><abstract>We present a new smoothing Newton method for nonlinear complementarity problems (NCP(F)) by using an NCP function to reformulate the problem to its equivalent form. Compared with most current smoothing methods, our method contains an estimating technique based on the active-set strategy. This technique focuses on the identification of the degenerate set for a solution
x
∗
of the NCP(F). The proposed method has the global convergence, each accumulation point is a solution of the problem. The introduction of the active-set strategy effectively reduces the scale of the problem. Under some regularity assumption, the degenerate set can be identified correctly near the solution and local superlinear convergence is obtained as well.</abstract><cop>Kidlington</cop><pub>Elsevier B.V</pub><doi>10.1016/j.cam.2010.05.004</doi><tpages>12</tpages><oa>free_for_read</oa></addata></record> |
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| identifier | ISSN: 0377-0427 |
| ispartof | Journal of computational and applied mathematics, 2010-10, Vol.234 (12), p.3424-3435 |
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| language | eng |
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| source | Elsevier ScienceDirect Journals; Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals |
| subjects | Convergence Degenerate indices Equivalence Exact sciences and technology Global analysis, analysis on manifolds Global convergence Mathematical analysis Mathematical models Mathematics Newton methods Nonlinear algebraic and transcendental equations Nonlinear complementarity problems Nonlinearity Numerical analysis Numerical analysis. Scientific computation Regularity Sciences and techniques of general use Smoothing Smoothing methods Strategy Superlinear convergence Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds |
| title | Smoothing Newton method for NCP with the identification of degenerate indices |
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