Second-order weak composed epiderivatives and applications to optimalityconditions

Qilin Wang; Xiao-Bing Li; Guolin Yu

doi:10.3934/jimo.2013.9.455

Article Contents

2013, Volume 9, Issue 2: 455-470. Doi: 10.3934/jimo.2013.9.455

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Second-order weak composed epiderivatives and applications to optimality conditions

1.
College of Sciences, Chongqing Jiaotong University, Chongqing, 400074
2.
Research Institute of Information and System Computation Science, Beifang University of Nationalities, Yinchuan, 750021

Received: March 31, 2011

Revised: December 31, 2012

Published: March 2013

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Abstract

In this paper, one introduces the second-order weak composed contingent epiderivative of set-valued maps, and discusses some of its properties. Then, by virtue of the second-order weak composed contingent epiderivative, necessary optimality conditions and sufficient optimality conditions are obtained for set-valued optimization problems. As consequences, recent existing results are derived. Several examples are provided to show the main results obtained.

Keywords:

Set-valued optimization,
second-order weak composed contingent epiderivatives,
second-order optimality conditions.

Mathematics Subject Classification: 90C26, 90C46.

Citation:

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References

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