Higher-order weakly generalized epiderivatives and applications to optimality conditions (Q443031)
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scientific article; zbMATH DE number 6063451
| Language | Label | Description | Also known as |
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| English | Higher-order weakly generalized epiderivatives and applications to optimality conditions |
scientific article; zbMATH DE number 6063451 |
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Higher-order weakly generalized epiderivatives and applications to optimality conditions (English)
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6 August 2012
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Summary: The notions of higher-order weakly generalized contingent epiderivative and higher-order weakly generalized adjacent epiderivative for set-valued maps are proposed. By virtue of the higher-order weakly generalized contingent (adjacent) epiderivatives, both necessary and sufficient optimality conditions are obtained for Henig efficient solutions to a set-valued optimization problem whose constraint set is determined by a set-valued map. The imposed assumptions are relaxed in comparison with those of recent results in the literature. Examples are provided to show some advantages of our notions and results.
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higher-order weakly generalized contingent epiderivative
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higher-order weakly generalized adjacent epiderivative
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set-valued maps
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necessary and sufficient optimality conditions
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Henig efficient solution
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