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Second order necessary conditions in set constrained differentiable vector optimization

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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.

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Correspondence to Vicente Novo.

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Mathematics subject classification 2000: 90C29, 90C46

This research was partially supported by Ministerio de Ciencia y Tecnología (Spain), project BMF2003-02194.

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Jiménez, B., Novo, V. Second order necessary conditions in set constrained differentiable vector optimization. Math Meth Oper Res 58, 299–317 (2003).

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