向量优化问题严格有效性的二阶最优性条件  

Second-order optimality conditions for strict efficiency of vector optimization problems

作　　者：朱胜坤[1] 彭兴媛[1] 刘琼荪[1] 

机构地区：[1]重庆大学数学与统计学院,重庆401331

出　　处：《云南大学学报（自然科学版）》2011年第3期257-263,270,共8页Journal of Yunnan University(Natural Sciences Edition)

基　　金：中央高校基本科研业务费资助项目(CDJXS11100036)

摘　　要：利用约束集的相依锥以及线性锥,结合凸集分离定理,在适当的正则性条件下得到了一类带字典序的向量优化问题的Lagrange乘子法则,并在此基础上提出了Lagrangian函数的概念.同时,利用Lagrangian函数建立了向量优化问题严格有效性的二阶最优性条件.By using the concepts of contingent cone and linearizing cone of a constraint set,together with a separation theorem for convex sets,the Lagrange multiplier rule for a kind vector optimization problem with lexicographic order was obtained,and on that basis,the concept of Lagrangian function was proposed.Simultaneously,in terms of the Lagrangian function,some second-order optimality conditions for strict efficiency of vector optimization problems were established.

关 键 词：正则性条件 Lagrange乘子法则 严格有效性 向量优化 二阶最优性条件 

分 类 号：O221.6[理学—运筹学与控制论]