First and second order sufficient conditions for strict minimality in nonsmooth vector optimization |
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Authors: | Bienvenido Jiménez |
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Institution: | a Departamento de Econom?́a e Historia Económica, Facultad de Econom?́a y Empresa, Universidad de Salamanca, Campus Miguel de Unamuno, s/n, 37007 Salamanca, Spain b Departamento de Matemática Aplicada, ETSI Industriales, Universidad Nacional de Educación a Distancia, Calle Juan del Rosal, 12, Ciudad Universitaria, Apartado 60149, 28080 Madrid, Spain |
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Abstract: | In this paper we present first and second order sufficient conditions for strict local minima of orders 1 and 2 to vector optimization problems with an arbitrary feasible set and a twice directionally differentiable objective function. With this aim, the notion of support function to a vector problem is introduced, in such a way that the scalar case and the multiobjective case, in particular, are contained. The obtained results extend the multiobjective ones to this case. Moreover, specializing to a feasible set defined by equality, inequality, and set constraints, first and second order sufficient conditions by means of Lagrange multiplier rules are established. |
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Keywords: | Vector optimization Strict local minimum First and second order sufficient optimality conditions Support function |
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