1) Benson proper efficient solution
Benson真有效解
1.
Benson proper efficient solution for vector extremum problems is the most important aspect of optimization problems,and it has drawn lots of attention.
向量极值问题的Benson真有效解,是优化问题的一个最重要的方面,吸引了许多关注的目光。
2.
Using vector closure,Benson proper efficient solution of set-valued optimization is introduced.
利用向量闭包,引进了集值优化的Benson真有效解。
2) Benson proper solution
Benson真有效解
1.
Benson proper solution in vector optimization;
向量优化问题的Benson真有效解
2.
The relation of Benson proper solution and the optimal solutions of scalarization problems is studied,and necessary and sufficiate conditions for Benson proper solution are obtaioned.
获得了 Benson真有效解的充分条件与必要条件 。
3) Benson proper efficiency
Benson真有效
1.
Generalized optimality conditions of set-valued optimization problems with Benson proper efficiency;
集值优化问题的Benson真有效解的广义最优性条件
2.
The concepts of (1,α)- order Clarke tangent derivative, (1,α)- order adjacent tangent derivative and (1,α)- order contingent tangent derivative for a set-valued map with respect to cone are introduced; Applying this, the generalized Kuhn-Tucker optimality conditions for set-valued optimization problems with Benson proper efficiency are established.
引进了集值映射关于锥的(1,α)-阶Clarke切导数,(1,α)-阶Adjacent切导数,(1,α)-阶Contingent切导数概念;应用它们导出了具Slater约束规格的集值优化问题的Benson真有效解的广义Kuhn-Tucker最优性条件。
3.
Hence the derivative type Kuhn-Tucker optimality condition for constrained vector set-valued optimization with Benson proper efficiency solutions is established.
本文引入了关于集值映射的α-阶Clarke切导数、α-阶邻接切导数及α-阶 伴随切导数的概念,借此建立了约束向量集值优化Benson真有效解导数型的Kuhn- Tucker条件。
4) Benson proper efficiency
Benson真有效性
1.
Benson proper efficiency in vector optimization with set-valued maps
集值向量优化的Benson真有效性
2.
Some characterizations of the benson proper efficiency under this generalized cone-subconvex like set-valued maps are established in terms of scalarization.
研究一类广义锥次似凸集值映射向量优化问题,首先建立一个择一定理,然后,讨论了标量下关于此类问题的Benson真有效性的一些性质。
3.
The concept and these resultsare then applied to study Benson proper efficiency for a vector optimization problem withset-valued maps in topological vector spaces.
然后，利用这些概念与结果来研究拓扑线性空间中带集值映射的向量优化问题的Benson真有效性，获得两个标量化结果和两个Lagrange乘子定理。
5) properly efficient solution
真有效解
1.
Then, sufficient condition and necessary condition for a properly efficient solution in the sense of Geoffrion are proved.
然后,证明了该多目标分式规划问题在Geoffrion意义下的真有效解的充分条件和必要条件。
2.
Considering the Wolfe type and Mond Weir type duals for a class of multiobjective variational problems discussed in paper 1 ,a general dual of such a multiobjective variational problem was proposed,and the corresponding weak and strong duality theorems with respect to properly efficient solutions were proved.
考虑文章〔１〕讨论的一类多目标变分问题的Ｗｏｌｆｅ型和Ｍｏｎｄ－Ｗｅｉｒ型对偶，对这样一类多目标变分问题提出一种一般对偶，鉴于在建立对偶问题时，如果把Ｇｅｏｆｒｉｏｎ参数作为变量，讨论关于真有效解的对偶性定理存在许多问题，对于预定的Ｇｅｏｆｒｉｏｎ参数，证明了关于真有效解的相应弱对偶定理和强对偶定
6) true effective solution
真有效解
1.
Generalized true effective solutions of problem of non-smooth vector extreme value;
非光滑向量极值问题的广义真有效解
补充资料：真解
1.犹彻悟。 2.独到而确切的见解。
说明：补充资料仅用于学习参考，请勿用于其它任何用途。
参考词条