1) necessary and sufficient optimality conditions
最优性充分和必要条件
1.
By transformalating the multi-objective fractional programming into an equivalent multi-objective programming,the necessary and sufficient optimality conditions of Fritz John and Kuhn Tucker type are obtained.
通过将多目标分式规划问题转化为多目标规划问题获得了Fritz John and Kuhn Tucker类型最优性充分和必要条件。
2) necessary optimality condition
最优性必要条件
1.
The Kuhn-Tucker type necessary optimality conditions under this constraint qualification are derived.
对一类目标函数由可微函数与凸函数之和组成、约束条件由Rn的凸子集X上的可微非线性不等式组成的不可微规划问题,提出了一个Abadie型约束品性,证明了该约束品性弱于文献[1]中的两个约束品性,得到了该约束品性下的Kuhn-Tucker型最优性必要条件。
3) necessary optimality conditions
最优性必要条件
1.
A note on necessary optimality conditions for a class of generalized fractional programming;
一类广义分式规划最优性必要条件的注记
2.
In this paper, the necessary optimality conditions for vector extremum problems with equality constraint in product of Banach spaces are obtained by using a implicit function theorem in Banach spaces and a theorem of the alternative for subconvexlike vector-valued maps in ordered linear topological spaces.
本文利用Banach空间中的隐函数定理和序线性拓扑空间中对于次似凸向量值映射的择一定理,得出了乘积Banach空间中具有等式约束向量极值问题的若干最优性必要条件。
3.
In this paper,by using a implicit function theorem in Banach spaces the necessary optimality conditions for mathematical programming problems with equality constraints in the product of Banach spaces are established.
本文利用 Banach 空间中的隐函数定理,得出了乘积 Banach 空间中具有一般等式约束的数学规划问题的最优性必要条件。
4) necessary optimality condition
必要最优性条件
1.
Moreover,the necessary optimality conditions in mathematical programming problem with equality and inequality constraints of Lipschitz functions are derived with the help of Ekeland variational principle on Riemannian manifolds.
在此基础上,利用Ekeland变分原理,推导出基于黎曼流形上具有等式和不等式约束的数学规划问题的必要最优性条件。
5) Fritz John necessary optimality condition
FritzJohn必要最优性条件
6) sufficient optimality conditions
最优性充分条件
1.
Finally, the sufficient optimality conditions of multiobjective programming are obtained by applying generalized (F,α,ρ,d)-convexity.
本文在 (F,α,ρ,d) -凸的基础上引进了广义 (F,α,ρ,d) -凸 ,并在此基础上获得了多目标规划的有效解的最优性充分条件 。
2.
In this paper,a class of multiobjective semi-infinite fractional programming problems involving(F,α,ρ,d)-invex functions are considered,some sufficient optimality conditions for the class of programming are derived.
本文考虑了一类(F,α,ρ,d)-凸下的多目标半无限分式规划问题,得到了这类规划问题的一些最优性充分条件。
补充资料：充分又必要条件
如果有甲必有乙，无甲必无乙，那么甲就是乙的充分又必要条件。例如，三角形是等角的，则三角形是等边的，而只有三角形是等角的，三角形才是等边的。因此，三角形等角就是三角形等边的充分又必要条件。
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