Journal of Applied Mathematics
- J. Appl. Math.
- Volume 2012 (2012), Article ID 691018, 19 pages.
Higher-Order Weakly Generalized Epiderivatives and Applications to Optimality Conditions
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.
J. Appl. Math., Volume 2012 (2012), Article ID 691018, 19 pages.
First available in Project Euclid: 14 December 2012
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Wang, Qilin; Yu, Guolin. Higher-Order Weakly Generalized Epiderivatives and Applications to Optimality Conditions. J. Appl. Math. 2012 (2012), Article ID 691018, 19 pages. doi:10.1155/2012/691018. https://projecteuclid.org/euclid.jam/1355495152