Optimality Conditions in Differentiable Vector Optimization via Second-Order Tangent Sets

被引：0

作者：

Bienvenido Jiménez

Vicente Novo

机构：

[1] Departamento de Economía e Historia Económica,

[2] Facultad de Economía y Empresa,undefined

[3] Universidad de Salamanca,undefined

[4] Campus Miguel de Unamuno,undefined

[5] s/n,undefined

[6] 37007 Salamanca,undefined

[7] Departamento de Matemática Aplicada,undefined

[8] E.T.S.I. Industriales,undefined

[9] UNED,undefined

[10] c/ Juan del Rosal 12,undefined

[11] Apartado 60149,undefined

[12] 28080 Madrid,undefined

来源：

Applied Mathematics and Optimization | 2004年 / 49卷

关键词：

Vector optimization; Second-order optimality conditions for efficiency; Second-order tangent set; Asymptotic second-order cone; Projective tangent set; Lagrange multipliers; Strict efficiency;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

We provide second-order necessary and sufficient conditions for a point to be an efficient element of a set with respect to a cone in a normed space, so that there is only a small gap between necessary and sufficient conditions. To this aim, we use the common second-order tangent set and the asymptotic second-order cone utilized by Penot. As an application we establish second-order necessary conditions for a point to be a solution of a vector optimization problem with an arbitrary feasible set and a twice Fréchet differentiable objective function between two normed spaces. We also establish second-order sufficient conditions when the initial space is finite-dimensional so that there is no gap with necessary conditions. Lagrange multiplier rules are also given.

引用

页码：123 / 144

页数：21