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**Higher-order weakly generalized epiderivatives and applications to optimality conditions.**
*(English)*
Zbl 1245.49030

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.

### MSC:

49J53 | Set-valued and variational analysis |

49K27 | Optimality conditions for problems in abstract spaces |

### Keywords:

higher-order weakly generalized contingent epiderivative; higher-order weakly generalized adjacent epiderivative; set-valued maps; necessary and sufficient optimality conditions; Henig efficient solution
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\textit{Q. Wang} and \textit{G. Yu}, J. Appl. Math. 2012, Article ID 691018, 19 p. (2012; Zbl 1245.49030)

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### References:

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