Second-Order Necessary Conditions, Constraint Qualifications and Exact Penalty for Mathematical Programs with Switching Constraints
In this paper, we investigate second-order necessary conditions and exact penalty of mathematical programs with switching constraints (MPSC). Some new second-order constraint qualifications and second-order quasi-normality are introduced for (MPSC), which are crucial to establish the second-order ne...
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| creator | Chen, Jiawei Liu, Luyu Lv, Yibing Zhao, Kequan |
| description | In this paper, we investigate second-order necessary conditions and exact
penalty of mathematical programs with switching constraints (MPSC). Some new
second-order constraint qualifications and second-order quasi-normality are
introduced for (MPSC), which are crucial to establish the second-order
necessary conditions and the error bound of (MPSC). We explore the relations
among these constraint qualifications in term of (MPSC). The characterizations
of Mordukhovich stationary point and strong stationary point of (MPSC) are
derived under some mild conditions. A sufficient condition is provided for a
Mordukhovich stationary point of (MPSC) being a strong stationary point. The
strong second-order necessary conditions as well as weak second-order necessary
conditions of (MPSC) are established under these weak constraint
qualifications. Finally, we obtain the local exact penalty of (MPSC) under the
local error bound or some constraint qualifications in term of (MPSC). |
| doi_str_mv | 10.48550/arxiv.2407.17285 |
| format | Article |
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penalty of mathematical programs with switching constraints (MPSC). Some new
second-order constraint qualifications and second-order quasi-normality are
introduced for (MPSC), which are crucial to establish the second-order
necessary conditions and the error bound of (MPSC). We explore the relations
among these constraint qualifications in term of (MPSC). The characterizations
of Mordukhovich stationary point and strong stationary point of (MPSC) are
derived under some mild conditions. A sufficient condition is provided for a
Mordukhovich stationary point of (MPSC) being a strong stationary point. The
strong second-order necessary conditions as well as weak second-order necessary
conditions of (MPSC) are established under these weak constraint
qualifications. Finally, we obtain the local exact penalty of (MPSC) under the
local error bound or some constraint qualifications in term of (MPSC).</description><identifier>DOI: 10.48550/arxiv.2407.17285</identifier><language>eng</language><subject>Mathematics - Optimization and Control</subject><creationdate>2024-07</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,885</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/2407.17285$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2407.17285$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Chen, Jiawei</creatorcontrib><creatorcontrib>Liu, Luyu</creatorcontrib><creatorcontrib>Lv, Yibing</creatorcontrib><creatorcontrib>Zhao, Kequan</creatorcontrib><title>Second-Order Necessary Conditions, Constraint Qualifications and Exact Penalty for Mathematical Programs with Switching Constraints</title><description>In this paper, we investigate second-order necessary conditions and exact
penalty of mathematical programs with switching constraints (MPSC). Some new
second-order constraint qualifications and second-order quasi-normality are
introduced for (MPSC), which are crucial to establish the second-order
necessary conditions and the error bound of (MPSC). We explore the relations
among these constraint qualifications in term of (MPSC). The characterizations
of Mordukhovich stationary point and strong stationary point of (MPSC) are
derived under some mild conditions. A sufficient condition is provided for a
Mordukhovich stationary point of (MPSC) being a strong stationary point. The
strong second-order necessary conditions as well as weak second-order necessary
conditions of (MPSC) are established under these weak constraint
qualifications. Finally, we obtain the local exact penalty of (MPSC) under the
local error bound or some constraint qualifications in term of (MPSC).</description><subject>Mathematics - Optimization and Control</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNqFjrsOgkAQRbexMOoHWDkfoAgIkZ5obHwFezJZFpkEds3s-qr9cZFY2NnMTO49mRwhxoHvRUkc-3PkB928MPKXXrAMk7gvXpmSRhezPReKYaekshb5CWkbkiOj7fRzW8dI2sHxijWVJLGrAHUBqwdKBwelsXZPKA3DFl2lmhaRWMOBzZmxsXAnV0HWTlmRPv88tUPRK7G2avTdAzFZr07pZtbp5hemplXKP9p5p734T7wB11hQgQ</recordid><startdate>20240724</startdate><enddate>20240724</enddate><creator>Chen, Jiawei</creator><creator>Liu, Luyu</creator><creator>Lv, Yibing</creator><creator>Zhao, Kequan</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20240724</creationdate><title>Second-Order Necessary Conditions, Constraint Qualifications and Exact Penalty for Mathematical Programs with Switching Constraints</title><author>Chen, Jiawei ; Liu, Luyu ; Lv, Yibing ; Zhao, Kequan</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-arxiv_primary_2407_172853</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Mathematics - Optimization and Control</topic><toplevel>online_resources</toplevel><creatorcontrib>Chen, Jiawei</creatorcontrib><creatorcontrib>Liu, Luyu</creatorcontrib><creatorcontrib>Lv, Yibing</creatorcontrib><creatorcontrib>Zhao, Kequan</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Chen, Jiawei</au><au>Liu, Luyu</au><au>Lv, Yibing</au><au>Zhao, Kequan</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Second-Order Necessary Conditions, Constraint Qualifications and Exact Penalty for Mathematical Programs with Switching Constraints</atitle><date>2024-07-24</date><risdate>2024</risdate><abstract>In this paper, we investigate second-order necessary conditions and exact
penalty of mathematical programs with switching constraints (MPSC). Some new
second-order constraint qualifications and second-order quasi-normality are
introduced for (MPSC), which are crucial to establish the second-order
necessary conditions and the error bound of (MPSC). We explore the relations
among these constraint qualifications in term of (MPSC). The characterizations
of Mordukhovich stationary point and strong stationary point of (MPSC) are
derived under some mild conditions. A sufficient condition is provided for a
Mordukhovich stationary point of (MPSC) being a strong stationary point. The
strong second-order necessary conditions as well as weak second-order necessary
conditions of (MPSC) are established under these weak constraint
qualifications. Finally, we obtain the local exact penalty of (MPSC) under the
local error bound or some constraint qualifications in term of (MPSC).</abstract><doi>10.48550/arxiv.2407.17285</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Optimization and Control |
| title | Second-Order Necessary Conditions, Constraint Qualifications and Exact Penalty for Mathematical Programs with Switching Constraints |
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