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April  2013, 9(2): 455-470. doi: 10.3934/jimo.2013.9.455

## Second-order weak composed epiderivatives and applications to optimality conditions

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

Received  April 2011 Revised  January 2013 Published  February 2013

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.
Citation: Qilin Wang, Xiao-Bing Li, Guolin Yu. Second-order weak composed epiderivatives and applications to optimality conditions. Journal of Industrial & Management Optimization, 2013, 9 (2) : 455-470. doi: 10.3934/jimo.2013.9.455
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