On Types of Isolated KKT Points in Polynomial Optimization
Let f be a real polynomial function with n variables and S be a basic closed semialgebraic set in ℝ n . In this paper, the authors are interested in the problem of identifying the type (local minimizer, maximizer or not extremum point) of a given isolated KKT point x* of f over S . To this end, the...
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| Veröffentlicht in: | Journal of systems science and complexity 2023-10, Vol.36 (5), p.2186-2213 |
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| container_title | Journal of systems science and complexity |
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| creator | Guo, Feng Jiao, Liguo Kim, Do Sang Pham, Tien-Son |
| description | Let
f
be a real polynomial function with
n
variables and
S
be a basic closed semialgebraic set in ℝ
n
. In this paper, the authors are interested in the problem of identifying the type (local minimizer, maximizer or not extremum point) of a given isolated KKT point
x*
of
f
over
S
. To this end, the authors investigate some properties of the tangency variety of
f
on
S
at
x*
, by which the authors introduce the definition of
faithful radius
of
f
over
S
at
x*
. Then, the authors show that the type of
x*
can be determined by the global extrema of
f
over the intersection of
S
and the Euclidean ball centered at
x*
with a faithful radius. Finally, the authors propose an algorithm involving algebraic computations to compute a faithful radius of
x*
and determine its type. |
| doi_str_mv | 10.1007/s11424-023-2119-7 |
| format | Article |
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f
be a real polynomial function with
n
variables and
S
be a basic closed semialgebraic set in ℝ
n
. In this paper, the authors are interested in the problem of identifying the type (local minimizer, maximizer or not extremum point) of a given isolated KKT point
x*
of
f
over
S
. To this end, the authors investigate some properties of the tangency variety of
f
on
S
at
x*
, by which the authors introduce the definition of
faithful radius
of
f
over
S
at
x*
. Then, the authors show that the type of
x*
can be determined by the global extrema of
f
over the intersection of
S
and the Euclidean ball centered at
x*
with a faithful radius. Finally, the authors propose an algorithm involving algebraic computations to compute a faithful radius of
x*
and determine its type.</description><identifier>ISSN: 1009-6124</identifier><identifier>EISSN: 1559-7067</identifier><identifier>DOI: 10.1007/s11424-023-2119-7</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Algorithms ; Complex Systems ; Control ; Mathematics ; Mathematics and Statistics ; Mathematics of Computing ; Operations Research/Decision Theory ; Optimization ; Polynomials ; Statistics ; Systems Theory</subject><ispartof>Journal of systems science and complexity, 2023-10, Vol.36 (5), p.2186-2213</ispartof><rights>The Editorial Office of JSSC & Springer-Verlag GmbH Germany 2023</rights><rights>The Editorial Office of JSSC & Springer-Verlag GmbH Germany 2023.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c268t-aec2fe53c9506e56f553644462d5887753d859cd3e69bf2633d0f17cd606ce633</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/s11424-023-2119-7$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s11424-023-2119-7$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Guo, Feng</creatorcontrib><creatorcontrib>Jiao, Liguo</creatorcontrib><creatorcontrib>Kim, Do Sang</creatorcontrib><creatorcontrib>Pham, Tien-Son</creatorcontrib><title>On Types of Isolated KKT Points in Polynomial Optimization</title><title>Journal of systems science and complexity</title><addtitle>J Syst Sci Complex</addtitle><description>Let
f
be a real polynomial function with
n
variables and
S
be a basic closed semialgebraic set in ℝ
n
. In this paper, the authors are interested in the problem of identifying the type (local minimizer, maximizer or not extremum point) of a given isolated KKT point
x*
of
f
over
S
. To this end, the authors investigate some properties of the tangency variety of
f
on
S
at
x*
, by which the authors introduce the definition of
faithful radius
of
f
over
S
at
x*
. Then, the authors show that the type of
x*
can be determined by the global extrema of
f
over the intersection of
S
and the Euclidean ball centered at
x*
with a faithful radius. Finally, the authors propose an algorithm involving algebraic computations to compute a faithful radius of
x*
and determine its type.</description><subject>Algorithms</subject><subject>Complex Systems</subject><subject>Control</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Mathematics of Computing</subject><subject>Operations Research/Decision Theory</subject><subject>Optimization</subject><subject>Polynomials</subject><subject>Statistics</subject><subject>Systems Theory</subject><issn>1009-6124</issn><issn>1559-7067</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><recordid>eNp1kMtKAzEUhoMoWKsP4C7gOprL5OZOijdaqIu6DmMmkZRpMibTRX16U0Zw5er8B_4LfABcE3xLMJZ3hZCGNghThighGskTMCOcV4GFPK0aY40Eoc05uChlizETGqsZuF9HuDkMrsDk4WtJfTu6Di6XG_iWQhwLDLGq_hDTLrQ9XA9j2IXvdgwpXoIz3_bFXf3eOXh_etwsXtBq_fy6eFghS4UaUess9Y4zqzkWjgvPORNN0wjacaWk5KxTXNuOOaE_PBWMddgTaTuBhXX1nYObqXfI6Wvvymi2aZ9jnTRUSU0UZ1pVF5lcNqdSsvNmyGHX5oMh2BwRmQmRqYjMEZGRNUOnTKne-OnyX_P_oR-04Gcf</recordid><startdate>20231001</startdate><enddate>20231001</enddate><creator>Guo, Feng</creator><creator>Jiao, Liguo</creator><creator>Kim, Do Sang</creator><creator>Pham, Tien-Son</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20231001</creationdate><title>On Types of Isolated KKT Points in Polynomial Optimization</title><author>Guo, Feng ; Jiao, Liguo ; Kim, Do Sang ; Pham, Tien-Son</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c268t-aec2fe53c9506e56f553644462d5887753d859cd3e69bf2633d0f17cd606ce633</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Algorithms</topic><topic>Complex Systems</topic><topic>Control</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Mathematics of Computing</topic><topic>Operations Research/Decision Theory</topic><topic>Optimization</topic><topic>Polynomials</topic><topic>Statistics</topic><topic>Systems Theory</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Guo, Feng</creatorcontrib><creatorcontrib>Jiao, Liguo</creatorcontrib><creatorcontrib>Kim, Do Sang</creatorcontrib><creatorcontrib>Pham, Tien-Son</creatorcontrib><collection>CrossRef</collection><jtitle>Journal of systems science and complexity</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Guo, Feng</au><au>Jiao, Liguo</au><au>Kim, Do Sang</au><au>Pham, Tien-Son</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On Types of Isolated KKT Points in Polynomial Optimization</atitle><jtitle>Journal of systems science and complexity</jtitle><stitle>J Syst Sci Complex</stitle><date>2023-10-01</date><risdate>2023</risdate><volume>36</volume><issue>5</issue><spage>2186</spage><epage>2213</epage><pages>2186-2213</pages><issn>1009-6124</issn><eissn>1559-7067</eissn><abstract>Let
f
be a real polynomial function with
n
variables and
S
be a basic closed semialgebraic set in ℝ
n
. In this paper, the authors are interested in the problem of identifying the type (local minimizer, maximizer or not extremum point) of a given isolated KKT point
x*
of
f
over
S
. To this end, the authors investigate some properties of the tangency variety of
f
on
S
at
x*
, by which the authors introduce the definition of
faithful radius
of
f
over
S
at
x*
. Then, the authors show that the type of
x*
can be determined by the global extrema of
f
over the intersection of
S
and the Euclidean ball centered at
x*
with a faithful radius. Finally, the authors propose an algorithm involving algebraic computations to compute a faithful radius of
x*
and determine its type.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/s11424-023-2119-7</doi><tpages>28</tpages></addata></record> |
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| identifier | ISSN: 1009-6124 |
| ispartof | Journal of systems science and complexity, 2023-10, Vol.36 (5), p.2186-2213 |
| issn | 1009-6124 1559-7067 |
| language | eng |
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| source | Alma/SFX Local Collection; SpringerLink Journals - AutoHoldings |
| subjects | Algorithms Complex Systems Control Mathematics Mathematics and Statistics Mathematics of Computing Operations Research/Decision Theory Optimization Polynomials Statistics Systems Theory |
| title | On Types of Isolated KKT Points in Polynomial Optimization |
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