吉林大学学报（理学版）
吉林大學學報（理學版）
길림대학학보（이학판）
JOURNAL OF JILIN UNIVERSITY(SCIENCE EDITION)
2014年
5期
943-948
,共6页
二阶渐近切锥%二阶渐近切上图导数%局部严有效元
二階漸近切錐%二階漸近切上圖導數%跼部嚴有效元
이계점근절추%이계점근절상도도수%국부엄유효원
second-order asymptotic tangent cone%second-order asymptotic epiderivative%locally strictly efficient element
在实赋范线性空间中利用新定义的二阶渐近切上图导数研究集值优化问题的严有效性。通过二阶渐近切锥引进一种新的二阶渐近切上图导数，给出一个例子说明它的存在条件比二阶渐近切导数存在条件更弱，并利用此导数及扩张锥的性质给出了集值优化问题取得局部严有效元的必要条件。
在實賦範線性空間中利用新定義的二階漸近切上圖導數研究集值優化問題的嚴有效性。通過二階漸近切錐引進一種新的二階漸近切上圖導數，給齣一箇例子說明它的存在條件比二階漸近切導數存在條件更弱，併利用此導數及擴張錐的性質給齣瞭集值優化問題取得跼部嚴有效元的必要條件。
재실부범선성공간중이용신정의적이계점근절상도도수연구집치우화문제적엄유효성。통과이계점근절추인진일충신적이계점근절상도도수，급출일개례자설명타적존재조건비이계점근절도수존재조건경약，병이용차도수급확장추적성질급출료집치우화문제취득국부엄유효원적필요조건。
The strict efficiency of set-valued optimization was considered in real normed linear space by a new second-order asymptotic epiderivative.With the help of second-order asymptotic tangent cone, a new second-order asymptotic epiderivative was introduced.At the same time,an example was given to show that its existence condition is weaker than that of second-order asymptotic tangent derivative. By applying the derivative and properties of a dilating cone,an optimality necessary condition of locally strictly efficient element for set-valued optimization was established.
