向量优化中Free Disposal集的某些对偶性质

Some dual characterizations of free disposal sets in vector optimization

在分离局部凸空间中考虑free disposal集的对偶性质,其中free disposal集是指与凸锥的代数和仍是其本身的集合.在E_1或E_2是free disposal集的条件下,证明了(E_1∩E_2)^+=E_1^++E_2^+和E_1^+∩E_2^+=(E_1+E_2)^+等对偶结果.

In this paper, we focus on some dual characterizations of free disposal sets in a separated locally convex space, in which, free disposal set means that its algebraic sum with a convex cone is still itself. Under the assumption that E1 or E2 is free disposal set, we proved some dual results, such as （El ∩E2）＋ = E1＋ ＋E2＋, E1＋∩ E2＋ = （El ＋E2）＋, etc.