An extension of the Basic Constraint Qualification to nonconvex vector optimization problems |
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Authors: | Bienvenido Jiménez Vicente Novo Miguel Sama |
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Institution: | 1. Departamento de Matemática Aplicada, E.T.S.I.I. Universidad Nacional de Educación a Distancia, Calle Juan del Rosal 12, 28040, Madrid, Spain
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Abstract: | In this paper a Basic Constraint Qualification is introduced for a nonconvex infinite-dimensional vector optimization problem extending the usual one from convex programming assuming the Hadamard differentiability of the maps. Corresponding KKT conditions are established by considering a decoupling of the constraint cone into half-spaces. This extension leads to generalized KKT conditions which are finer than the usual abstract multiplier rule. A second constraint qualification expressed directly in terms of the data is also introduced, which allows us to compute the contingent cone to the feasible set and, as a consequence, it is proven that this condition is a particular case of the first one. Relationship with other constraint qualifications in infinite-dimensional vector optimization, specially with the Kurcyuscz-Robinson-Zowe constraint qualification, are also given. |
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