Convergence analysis of a block improvement method for polynomial optimization over unit spheres
Summary In this paper, we study the convergence property of a block improvement method (BIM) for the bi‐quadratic polynomial optimization problem over unit spheres. We establish the global convergence of the method generally and establish its linear convergence rate under the second‐order sufficient...
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| Veröffentlicht in: | Numerical linear algebra with applications 2015-12, Vol.22 (6), p.1059-1076 |
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| container_title | Numerical linear algebra with applications |
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| creator | Wang, Yiju Caccetta, Louis Zhou, Guanglu |
| description | Summary
In this paper, we study the convergence property of a block improvement method (BIM) for the bi‐quadratic polynomial optimization problem over unit spheres. We establish the global convergence of the method generally and establish its linear convergence rate under the second‐order sufficient condition. We also extend the BIM to inhomogeneous polynomial optimization problems over unit spheres. Numerical results reported in this paper show that the method is promising. Copyright © 2015 John Wiley & Sons, Ltd. |
| doi_str_mv | 10.1002/nla.1996 |
| format | Article |
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In this paper, we study the convergence property of a block improvement method (BIM) for the bi‐quadratic polynomial optimization problem over unit spheres. We establish the global convergence of the method generally and establish its linear convergence rate under the second‐order sufficient condition. We also extend the BIM to inhomogeneous polynomial optimization problems over unit spheres. Numerical results reported in this paper show that the method is promising. Copyright © 2015 John Wiley & Sons, Ltd.</description><identifier>ISSN: 1070-5325</identifier><identifier>EISSN: 1099-1506</identifier><identifier>DOI: 10.1002/nla.1996</identifier><language>eng</language><publisher>Oxford: Blackwell Publishing Ltd</publisher><subject>bi-quadratic optimization ; block improvement method ; Blocking ; Convergence ; Linear algebra ; Mathematical models ; Online ; Optimization ; Polynomials</subject><ispartof>Numerical linear algebra with applications, 2015-12, Vol.22 (6), p.1059-1076</ispartof><rights>Copyright © 2015 John Wiley & Sons, Ltd.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c4346-cd32ba350315116cc42994cb551ffc195b863551990957d70da8088717cc51d3</citedby><cites>FETCH-LOGICAL-c4346-cd32ba350315116cc42994cb551ffc195b863551990957d70da8088717cc51d3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://onlinelibrary.wiley.com/doi/pdf/10.1002%2Fnla.1996$$EPDF$$P50$$Gwiley$$H</linktopdf><linktohtml>$$Uhttps://onlinelibrary.wiley.com/doi/full/10.1002%2Fnla.1996$$EHTML$$P50$$Gwiley$$H</linktohtml><link.rule.ids>314,780,784,1417,27924,27925,45574,45575</link.rule.ids></links><search><creatorcontrib>Wang, Yiju</creatorcontrib><creatorcontrib>Caccetta, Louis</creatorcontrib><creatorcontrib>Zhou, Guanglu</creatorcontrib><title>Convergence analysis of a block improvement method for polynomial optimization over unit spheres</title><title>Numerical linear algebra with applications</title><addtitle>Numer. Linear Algebra Appl</addtitle><description>Summary
In this paper, we study the convergence property of a block improvement method (BIM) for the bi‐quadratic polynomial optimization problem over unit spheres. We establish the global convergence of the method generally and establish its linear convergence rate under the second‐order sufficient condition. We also extend the BIM to inhomogeneous polynomial optimization problems over unit spheres. Numerical results reported in this paper show that the method is promising. Copyright © 2015 John Wiley & Sons, Ltd.</description><subject>bi-quadratic optimization</subject><subject>block improvement method</subject><subject>Blocking</subject><subject>Convergence</subject><subject>Linear algebra</subject><subject>Mathematical models</subject><subject>Online</subject><subject>Optimization</subject><subject>Polynomials</subject><issn>1070-5325</issn><issn>1099-1506</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2015</creationdate><recordtype>article</recordtype><recordid>eNp10FFLwzAQB_AiCuoU_AgBX3zpvDRN0zyOoVMZ-uBA32KWphpNk5p00_np7ZgoCj7dHfw47v5JcoRhiAGyU2flEHNebCV7GDhPMYVie90zSCnJ6G6yH-MzABSUk73kYezdUodH7ZRG0km7iiYiXyOJ5tarF2SaNvilbrTrUKO7J1-h2gfUertyvjHSIt92pjEfsjPeoZ4GtHCmQ7F90kHHg2Snljbqw686SGbnZ7PxRTq9mVyOR9NU5SQvUlWRbC4JBYIpxoVSecZ5ruaU4rpWmNN5WZB-4Bw4ZRWDSpZQlgwzpSiuyCA52aztr31d6NiJxkSlrZVO-0UUuATIS5YT2tPjP_TZL0L_eq8YZbTMciA_C1XwMQZdizaYRoaVwCDWSYs-abFOuqfphr4Zq1f_OnE9Hf32Jnb6_dvL8CIKRhgVd9cTwS7G7Cq7vxU5-QSsHI3z</recordid><startdate>201512</startdate><enddate>201512</enddate><creator>Wang, Yiju</creator><creator>Caccetta, Louis</creator><creator>Zhou, Guanglu</creator><general>Blackwell Publishing Ltd</general><general>Wiley Subscription Services, Inc</general><scope>BSCLL</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>201512</creationdate><title>Convergence analysis of a block improvement method for polynomial optimization over unit spheres</title><author>Wang, Yiju ; Caccetta, Louis ; Zhou, Guanglu</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c4346-cd32ba350315116cc42994cb551ffc195b863551990957d70da8088717cc51d3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2015</creationdate><topic>bi-quadratic optimization</topic><topic>block improvement method</topic><topic>Blocking</topic><topic>Convergence</topic><topic>Linear algebra</topic><topic>Mathematical models</topic><topic>Online</topic><topic>Optimization</topic><topic>Polynomials</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Wang, Yiju</creatorcontrib><creatorcontrib>Caccetta, Louis</creatorcontrib><creatorcontrib>Zhou, Guanglu</creatorcontrib><collection>Istex</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>Numerical linear algebra with applications</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Wang, Yiju</au><au>Caccetta, Louis</au><au>Zhou, Guanglu</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Convergence analysis of a block improvement method for polynomial optimization over unit spheres</atitle><jtitle>Numerical linear algebra with applications</jtitle><addtitle>Numer. Linear Algebra Appl</addtitle><date>2015-12</date><risdate>2015</risdate><volume>22</volume><issue>6</issue><spage>1059</spage><epage>1076</epage><pages>1059-1076</pages><issn>1070-5325</issn><eissn>1099-1506</eissn><abstract>Summary
In this paper, we study the convergence property of a block improvement method (BIM) for the bi‐quadratic polynomial optimization problem over unit spheres. We establish the global convergence of the method generally and establish its linear convergence rate under the second‐order sufficient condition. We also extend the BIM to inhomogeneous polynomial optimization problems over unit spheres. Numerical results reported in this paper show that the method is promising. Copyright © 2015 John Wiley & Sons, Ltd.</abstract><cop>Oxford</cop><pub>Blackwell Publishing Ltd</pub><doi>10.1002/nla.1996</doi><tpages>18</tpages></addata></record> |
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| language | eng |
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| subjects | bi-quadratic optimization block improvement method Blocking Convergence Linear algebra Mathematical models Online Optimization Polynomials |
| title | Convergence analysis of a block improvement method for polynomial optimization over unit spheres |
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