Higher-order optimality conditions for strict minimality in set-valued otimization (Q2884674)
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scientific article; zbMATH DE number 6039386
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Higher-order optimality conditions for strict minimality in set-valued otimization |
scientific article; zbMATH DE number 6039386 |
Statements
30 May 2012
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strict local minimizers of order \(m\)
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upper and lower Studniarski and Dini derivatives of set-valued maps
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constrained set-valued optimization problems
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higher-order necessary and sufficient optimality conditions
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Higher-order optimality conditions for strict minimality in set-valued otimization (English)
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The authors introduce \(m\)th order upper and lower Studniarski and Dini derivatives of set-mappings and give a relationship between them in case the mappings are Holder continuous. A constrained set-valued optimization problem together with the notion of strict local minimum of order m for this problem are introduced. Higher-order necessary and sufficient optimality conditions for strict local minima of order m are established in terms of these derivatives. Some illustrative examples are given as well.
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