集值优化问题严格有效解的一、二阶最优性条件

Acta mathematica scientia,Series A ›› 2014, Vol. 34 ›› Issue (1): 193-206.

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First and Second Order Optimality Conditions for Strict Minimality in Set-valued Optimization

LIU San-Yang, LI Jun

Department of Applied Mathematics, Xidian University, Xi'an |710071； School of Mathematics and Information, China West Normal University, Sichuan Nanchong |637002

Received:2012-04-07 Revised:2013-08-17 Online:2014-02-25 Published:2014-02-25
Supported by:
国家自然科学基金(61373174, 11371015)、教育部科学技术重点项目(211163)和四川省青年科技基金(2012JQ0032)资助.

Abstract

Abstract:

In this paper, the notion of local strict minimum of order m (m≥1) for vector optimization problems is extended
from single-valued maps to set-valued maps. Some properties and characterizations are then investigated in normed spaces. Furthermore, necessary and sufficient conditions for strict minimum of orders m≥1 are established by using Dini derivatives and support functions.

Key words: Set-valued optimization, First and second order optimality, Support function, Strict minimum, Dini derivative, Tangent cone

CLC Number:

90C25

CHAI Yan-Fei, LIU San-Yang, LI Jun. First and Second Order Optimality Conditions for Strict Minimality in Set-valued Optimization[J].Acta mathematica scientia,Series A, 2014, 34(1): 193-206.

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First and Second Order Optimality Conditions for Strict Minimality in Set-valued Optimization

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