Geodesic
Optimality conditions of first and second order in vector optimization problems on metric spaces
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 15 (2009) no. 4, pp. 32-43

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For mappings defined on metric spaces with values in Banach spaces, the notions of derivative vectors of first and second order are introduced. These notions are used to establish necessary conditions and sufficient conditions of first and second order for points of local $\prec$-minimum of such mappings, where $\prec$ is the strict preorder relation defined on the space of values of the mapping that is minimized. Minimality conditions are obtained as corollaries for the case when the mapping is defined on a subset of a normed space.
Keywords: ector optimization, metric spaces, conical local approximations of sets, derivatives of mappings. 
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     author = {V. I. Bakhtin and V. V. Gorokhovik},
     title = {Optimality conditions of first and second order in vector optimization problems on metric spaces},
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     pages = {32--43},
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     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2009_15_4_a3/}
}
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V. I. Bakhtin; V. V. Gorokhovik. Optimality conditions of first and second order in vector optimization problems on metric spaces. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 15 (2009) no. 4, pp. 32-43. http://geodesic.mathdoc.fr/item/TIMM_2009_15_4_a3/