First and second order optimality conditions for vector optimization problems on metric spaces

被引：0
|
作者：
V. I. Bakhtin
V. V. Gorokhovik
机构：
[1] National Academy of Sciences of Belarus,Institute of Mathematics
来源：
Proceedings of the Steklov Institute of Mathematics | 2010年 / 269卷
关键词：
vector optimization; metric spaces; conical local approximations of sets; derivatives of mappings;
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摘要：
For mappings defined on metric spaces and with values in Banach spaces, the notions of derivative vectors of first and second order are introduced. These notions are used to establish both necessary and sufficient optimality conditions of first and second order for local ≺-minimizers of such mappings, where ≺ is a strict preorder relation defined on the space of values of the mapping that is minimized. As corollaries of the above results, minimality conditions are also obtained for the case when the mapping is defined on a subset of a normed space.
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页码：28 / 39
页数：11
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