【摘要】 <正> 本文首先对于半序线性空间给出一个与凸集分离定理等价的定理,它对讨论凸向量规划的弱有效解问题是很方便的.本文的结论与史树中的结论完全平行.不过两篇文章是从不同的角度考虑问题,一个讨论绝对极值问题,另一个讨论相对极值问题;两篇文章,哪一篇都不能直接推出另一篇来.而且证明方法上很不一样.更多还原

【Abstract】 This paper gives a separation theorem of convex cone on an ordered vector space:Theorem.Let X be a linear space,Y an ordered vector space,and C(?)X×Y aconvex cone.Ifi)C~i(?);ii)(θ, y)∈C(?)y≮θ;iii)(?)∈Y,such that V_x={x∈X|(x,(?))∈C}is an absorbing set on X,then thereexi(?)ts a linear mapping ∧:X→Y,such that∧x+y≮0,(?)(x,y)∈C.This theorem is equivalent to usual separation theorems of convex sets,and can be used to ge-neralize Hahn-Ban(?)ch Theorem and obtain a result,correspo(?)ding to Kuhn-Tucker’s theoremof convex programming,for the weak efficient solution of the convex vector programming.更多还原