Second order necessary conditions in set constrained differentiable vector optimization |
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Authors: | Jiménez Bienvenido Novo Vicente |
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Affiliation: | (1) Departamento de Economía e Historia Económica, Facultad de Economía y Empresa, Universidad de Salamanca Campus Miguel de Unamuno s/n, 37007 Salamanca, Spain;(2) Departamento de Matemática Aplicada, UNED, ETSII c/ Juan del Rosal, 12, Ciudad Universitaria, Apartado 60149, 28080 Madrid, Spain |
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Abstract: | We state second order necessary optimality conditions for a vector optimization problem with an arbitrary feasible set and an order in the final space given by a pointed convex cone with nonempty interior. We establish, in finite-dimensional spaces, second order optimality conditions in dual form by means of Lagrange multipliers rules when the feasible set is defined by a function constrained to a set with convex tangent cone. To pass from general conditions to Lagrange multipliers rules, a generalized Motzkin alternative theorem is provided. All the involved functions are assumed to be twice Fréchet differentiable. Mathematics subject classification 2000: 90C29, 90C46This research was partially supported by Ministerio de Ciencia y Tecnología (Spain), project BMF2003-02194. |
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Keywords: | Multiobjective problems Second order necessary conditions for efficiency Lagrange multipliers Second order tangent set |
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