Second-Order Conditions for Open-Cone Minimizers and Firm Minimizers in Set-Valued Optimization Subject to Mixed Constraints
We consider second-order optimality conditions for set-valued optimization problems subject to mixed constraints. Such optimization models are useful in a wide range of practical applications. By using several kinds of derivatives, we obtain second-order necessary conditions for local Q -minimizers...
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| Veröffentlicht in: | Journal of optimization theory and applications 2016-10, Vol.171 (1), p.45-69 |
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| container_title | Journal of optimization theory and applications |
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| creator | Khanh, Phan Quoc Tung, Nguyen Minh |
| description | We consider second-order optimality conditions for set-valued optimization problems subject to mixed constraints. Such optimization models are useful in a wide range of practical applications. By using several kinds of derivatives, we obtain second-order necessary conditions for local
Q
-minimizers and local firm minimizers with attention to the envelope-like effect. Under the second-order Abadie constraint qualification, we get stronger necessary conditions. When the second-order Kurcyusz–Robinson–Zowe constraint qualification is imposed, our multiplier rules are of the Karush–Kuhn–Tucker type. Sufficient conditions for firm minimizers are established without any convexity assumptions. As an application, we extend and improve some recent existing results for nonsmooth mathematical programming. |
| doi_str_mv | 10.1007/s10957-016-0995-x |
| format | Article |
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Q
-minimizers and local firm minimizers with attention to the envelope-like effect. Under the second-order Abadie constraint qualification, we get stronger necessary conditions. When the second-order Kurcyusz–Robinson–Zowe constraint qualification is imposed, our multiplier rules are of the Karush–Kuhn–Tucker type. Sufficient conditions for firm minimizers are established without any convexity assumptions. As an application, we extend and improve some recent existing results for nonsmooth mathematical programming.</description><identifier>ISSN: 0022-3239</identifier><identifier>EISSN: 1573-2878</identifier><identifier>DOI: 10.1007/s10957-016-0995-x</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Applications of Mathematics ; Calculus of Variations and Optimal Control; Optimization ; Convexity ; Derivatives ; Engineering ; Mathematical programming ; Mathematics ; Mathematics and Statistics ; Multipliers ; Operations Research/Decision Theory ; Optimization ; Studies ; Theory of Computation</subject><ispartof>Journal of optimization theory and applications, 2016-10, Vol.171 (1), p.45-69</ispartof><rights>Springer Science+Business Media New York 2016</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c349t-70a5e79af5b3428ce18f53bc95b4f3a9949d07d3fc96dc671fc37023d9f687f73</citedby><cites>FETCH-LOGICAL-c349t-70a5e79af5b3428ce18f53bc95b4f3a9949d07d3fc96dc671fc37023d9f687f73</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/s10957-016-0995-x$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s10957-016-0995-x$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27903,27904,41467,42536,51297</link.rule.ids></links><search><creatorcontrib>Khanh, Phan Quoc</creatorcontrib><creatorcontrib>Tung, Nguyen Minh</creatorcontrib><title>Second-Order Conditions for Open-Cone Minimizers and Firm Minimizers in Set-Valued Optimization Subject to Mixed Constraints</title><title>Journal of optimization theory and applications</title><addtitle>J Optim Theory Appl</addtitle><description>We consider second-order optimality conditions for set-valued optimization problems subject to mixed constraints. Such optimization models are useful in a wide range of practical applications. By using several kinds of derivatives, we obtain second-order necessary conditions for local
Q
-minimizers and local firm minimizers with attention to the envelope-like effect. Under the second-order Abadie constraint qualification, we get stronger necessary conditions. When the second-order Kurcyusz–Robinson–Zowe constraint qualification is imposed, our multiplier rules are of the Karush–Kuhn–Tucker type. Sufficient conditions for firm minimizers are established without any convexity assumptions. 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Q
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| subjects | Applications of Mathematics Calculus of Variations and Optimal Control Optimization Convexity Derivatives Engineering Mathematical programming Mathematics Mathematics and Statistics Multipliers Operations Research/Decision Theory Optimization Studies Theory of Computation |
| title | Second-Order Conditions for Open-Cone Minimizers and Firm Minimizers in Set-Valued Optimization Subject to Mixed Constraints |
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