广义高阶锥方向导数及对集值优化的应用

Abstract

Abstract:

In this paper, a generalized higher-order contingent (adjacent) set for a set and a generalized higher-order cone-directed contingent (adjacent) derivative for a set-valued map are introduced. By virtue of the derivatives, generalized higher-order necessary and sufficient conditions are obtained for a set-valued optimization problem, whose constraint condition is determined by a fixed set or a set-valued map, respectively.

Key words: Generalized higher-order contingent (adjacent) sets, Generalized higher-order cone-directed contingent (adjacent) derivatives,
Set-valued optimization, Weak minimizer, Generalized higher-order optimality conditions

CLC Number:

90C26

WANG Qi-Lin, LI Shng-Jie. Generalized |Higher-order Cone-directed Derivatives and Applications to Set-valued Optimization[J].Acta mathematica scientia,Series A, 2011, 31(4): 902-909.

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Generalized |Higher-order Cone-directed Derivatives and Applications to Set-valued Optimization

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