集值向量优化问题超有效点的广义鞍点刻画  

Super efficient point in vector optimization problems with set-valued maps characterized by generalized saddle point

作　　者：余国林[1] 刘三阳[1] 

机构地区：[1]西安电子科技大学应用数学系

出　　处：《西北大学学报（自然科学版）》2007年第2期179-182,共4页Journal of Northwest University（Natural Science Edition）

基　　金：陕西省自然科学基金资助项目(2004A05)

摘　　要：目的研究局部凸空间中集值优化超有效解与鞍点之间的关系问题。方法通过广义鞍点的性质并结合择一定理,得到有关充分条件和必要条件。结果得到广义鞍点的一个锥分离性质,并且建立了近似锥-次类凸集值向量优化问题超有效解为广义鞍点的条件。结论其结果深化和丰富了最优化理论的内容。Aim In locally convex spaces, to study the relationships between the super efficient solution and gener- alized saddle point. Methods Using the properties of saddle point and alternative theorem, the sufficient and necessary conditions of a super efficient point being a generalized saddle point are obtained. Results The property of generalized saddle point with cone separation was prved and the conditions of super efficient solutions being the generalized saddle point in the nearly cone-subconvexlike vector optimization problems were set up with set-valued maps. Conclusion These results deepen and enrich the content of optimization theory.

关 键 词：近似锥-次类凸 集值映射 超有效性 广义鞍点 

分 类 号：O221.2[理学—运筹学与控制论]