Second order necessary conditions in set constrained differentiable vector optimization

Bienvenido Jiménez () and Vicente Novo ()

Mathematical Methods of Operations Research, 2003, vol. 58, issue 2, 299-317

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. Copyright Springer-Verlag 2003

Keywords: Multiobjective problems; Second order necessary conditions for efficiency; Lagrange multipliers; Second order tangent set (search for similar items in EconPapers)
Date: 2003
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DOI: 10.1007/s001860300283

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