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
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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.Abstract: 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.