拟不变凸集值优化问题严有效解的最优性条件  

Optimality Conditions for Strictly Efficient Solutions of Preinvex Set-valued Optimization

作　　者：谢燕霞[1] 徐义红[1] 汪涛[1] 

机构地区：[1]南昌大学数学系,南昌330031

出　　处：《应用泛函分析学报》2011年第4期398-404,共7页Acta Analysis Functionalis Applicata

基　　金：国家自然科学基金(10461007);江西省自然科学基金(2009GZS0021);江西省教育厅科技项目(GJJ09069)

摘　　要：在赋范线性空间中借助切导数研究集值优化问题的严有效性.当目标函数和约束函数相对于同一向量函数为拟不变凸时,利用凸集分离定理给出了集值优化问题取得严有效元的Kuhn-Tucker型最优性必要条件.利用切导数的性质,用构造性方法得到了拟不变凸集值优化问题取得严有效元的充分条件.In normed linear spaces, the set-valued optimization problem is considered in the sense of strictly efficiency with contingent tangent derivative. When both the objective function and constrained function are preinvex set-valued functions with respect to the same vector function, by applying separation theorem for convex sets, Kuhn-Tucker type necessary optimality condition is established for set-valued optimization problem to obtain its strictly efficient solutions. With properties of contingent tangent derivative, by using constructive method, the sufficiency optimality condition is also obtained.

关 键 词：拟不变凸函数 严有效解 集值优化 

分 类 号：O224[理学—运筹学与控制论]