Higher-Order Variational Sets and Higher-Order Optimality Conditions for Proper Efficiency in Set-Valued Nonsmooth Vector Optimization

P. Q. Khanh () and N. D. Tuan
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P. Q. Khanh: International University of Hochiminh City
N. D. Tuan: University of Natural Sciences of Hochiminh City

Journal of Optimization Theory and Applications, 2008, vol. 139, issue 2, No 3, 243-261

Abstract: Abstract Higher-order variational sets are proposed for set-valued mappings, which are shown to be more convenient than generalized derivatives in approximating mappings at a considered point. Both higher-order necessary and sufficient conditions for local Henig-proper efficiency, local strong Henig-proper efficiency and local λ-proper efficiency in set-valued nonsmooth vector optimization are established using these sets. The technique is simple and the results help to unify first and higher-order conditions. As consequences, recent existing results are derived. Examples are provided to show some advantages of our notions and results.

Keywords: Higher-order variational sets; Higher-order optimality conditions; Set-valued nonsmooth vector optimization; Local Henig-proper efficiency; Local strong Henig-proper efficiency; Local λ-proper efficiency (search for similar items in EconPapers)
Date: 2008
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Citations: View citations in EconPapers (6)

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DOI: 10.1007/s10957-008-9414-2

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