择一定理

First, under G -convexity, the alternative theorem is proved.

首先，在G-凸的条件下，证明了择一定理。

By the alternative theorem, the optimality conditions of vector extremum problems with generalized inequality constraint are established in linear space.

在线性空间中，定义了广义次似凸映射的概念，并讨论了它的一些性质，建立了此映射的择一定理。

Under the G-differentiable ,using the alternative theorem of generalized subconvexlike map and other some conclusions in locally-convex Hausdorff topological spaces, the optimality conditions of vector extremum problems with set constraint are established.

在局部凸Hausdorff拓扑空间中，在G-可微的意义下，运用广义次似凸映射的择一定理和其他一些结论，建立了带集合约束的向量极值问题的最优性条件。

Applying the theorem of alternative of subconvexlike map and other some conclusions, the optimality conditions represented by gradient for the vector extremum problems with generalized inequality constraint are obtained.

在线性拓扑空间中，引入了G-可微函数的梯度的概念，运用次似凸映射的择一定理和其他一些结论，获得了带广义不等式约束的向量极值问题的一种含有梯度的最优性条件。

In ordered linear topological space, the concept of (u,O_2,Y_ )- generalized subconvexlike map is defined, and some important properties of the concept are discussed, and the alternative theorem of the map is established.

在序线性拓扑空间中，定义了(u，0_2；Y_ )-广义次似凸映射的概念，并讨论了它的一些性质，建立了此映射的择一定理。

A theorem of the alternative for the generalized subconvexlike set-valued maps is established using the separation theorem of convex sets in a Banach spaces, the concept of weak Benson proper efficient elements for a vector optimization problem is introduced, and the optimality necessary and sufficient Lagrange conditions for a vector set-valued map constrained optimization problem with the weak Benson proper efficiency is developed, with which the optimality Lagrange conditions for a nonconvex vector top-base constrained optimization of set-valued maps with the Benson proper efficiency are obtained.

刘莹 ，刘三阳，盛宝怀运用凸集分离定理对广义锥次类凸集值映射建立了一种择一性定理。引入向量优化弱Benson真有效元的概念，对带约束的非凸向量集值优化问题建立了在弱Benson真有效意义下有效元应满足Lagrange乘子型的必要及充分条件，并用这一结果建立了多目标主从非凸向量集值优化在弱Benson真有效意义下最优解的Lagrange乘子型充要条件。

Then relative interior is introduced and an alternative theorem of generalized convex set-valued maps is established by using the separation theorem.

引进了相对内部，应用凸集分离定理建立了一个广义凸集值映射的择一性定理。

This paper deals with a class of singular Positone boundary value problems.

对一类具有奇性Positone边界值问题进行了研究，利用非线性二择一不动点定理建立了问题正解的3个存在性原则。

In the sense of weak effective solution,the problems of Lagrange duality and saddle point are discussed under the convexlike condition.An alternative theorem of the system containing a semidefinite constraint of a matrix function is established at first.

首先在似凸条件下建立了一个含矩阵函数半定约束系统的择一性定理，由此得到多目标半定规划及其在弱有效解意义下的Lagrange对偶理论，包括弱对偶、强对偶和逆对偶等。

We have no common name for a mime of Sophron or Xenarchus and a Socratic Conversation; and we should still be without one even if the imitation in the two instances were in trimeters or elegiacs or some other kind of verse--though it is the way with people to tack on 'poet' to the name of a metre, and talk of elegiac-poets and epic-poets, thinking that they call them poets not by reason of the imitative nature of their work, but indiscriminately by reason of the metre they write in.

索夫农 、森那库斯和苏格拉底式的对话采用的模仿没有一个公共的名称；三音步诗、挽歌体或其他类型的诗的模仿也没有——人们把&诗人&这一名词和格律名称结合到一起，称之为挽歌体诗人或者史诗诗人，他们被称为诗人，似乎只是因为遵守格律写作，而非他们作品的模仿本质。

The relationship between communicative competence and grammar teaching should be that of the ends and the means.

交际能力和语法的关系应该是目标与途径的关系。