New Second-Order Directional Derivative and Optimality Conditions in Scalar and Vector Optimization

被引：0
作者：
C. Gutiérrez
B. Jiménez
V. Novo
机构：
[1] Universidad de Valladolid,Departamento de Matemática Aplicada, E.T.S.I. Informática
[2] Universidad Nacional de Educación a Distancia,Departamento de Matemática Aplicada, E.T.S.I. Industriales
来源：
Journal of Optimization Theory and Applications | 2009年 / 142卷
关键词：
Second order directional derivative; Optimality conditions; Vector optimization; Scalarization; Second order tangent set;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We present a new second-order directional derivative and study its properties. Using this derivative and the parabolic second-order derivative, we establish second-order necessary and sufficient optimality conditions for a general scalar optimization problem by means of the asymptotic and parabolic second-order tangent sets to the feasible set. For the sufficient conditions, the initial space must be finite dimensional. Then, these conditions are applied to a general vector optimization problem obtaining second-order optimality conditions that generalize the differentiable case. For this aim, we introduce a scalarization, and the relationships between the different types of solutions to the vector optimization problem and the scalarized problem are studied.
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页码：85 / 106
页数：21
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