归纳极限下的非线性序锥与向量最优化
Non-Conflicting Ordering Cones and Vector Optimization in Inductive Limits
摘要：
设$(E,ξ)={\rm ind}(E_n, ξ_n)$是局部凸空间序列$(E_n, ξ_n)_{n\in N}$的归纳极限，且每一步$(E_n, ξ_n)$都被凸（实）锥$S_n$赋予偏序.在偏序局部凸空间的归纳极限框架下，引入了持久有效点、持久弱有效点和持久全局真有效点的概念.对于多个序锥，引入了非冲突的概念。在序锥序列$(S_n)_{n\in N}$不冲突的条件下，给出了持久弱有效点的存在性定理.由此得到了一个持久全局真有效点的存在性定理。
英文摘要：
Let $(E,ξ)={\rm ind}(E_n, ξ_n)$ be an inductive limit of a sequence $(E_n, ξ_n)_{n\in N}$ of locally convex spaces and let every step $(E_n, ξ_n)$ be endowed with a partial order by a pointed convex (solid) cone $S_n$. In the framework of inductive limits of partially ordered locally convex spaces, the notions of lastingly efficient points, lastingly weakly efficient points and lastingly globally properly efficient points are introduced. For several ordering cones, the notion of non-conflict is introduced. Under the requirement that the sequence $(S_n)_{n\in N}$ of ordering cones is non-conflicting, an existence theorem on lastingly weakly efficient points is presented. From this, an existence theorem on lastingly globally properly efficient points is deduced.
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