1) Kuhn-Tucker sufficient condition
Kuhn-Tucker型充分条件
1.
On the Kuhn-Tucker sufficient conditions for a class of nonsmooth generalized Fractional multiobjective programming;
一类非光滑多目标广义分式规划的Kuhn-Tucker型充分条件
2) the Kuhn-Tucker-type conditions
Kuhn-Tucker型条件
3) Kuhn-Tucker sufficient optimality conditions
Kuhn-Tucker最优性充分条件
1.
Kuhn-Tucker sufficient optimality conditions and weak duality results are obtained on(F,α,ρ,d)-convexity and generalized(F,α,ρ,d)-convexity.
在(F,α,,ρd)-凸和广义(F,α,,ρd)-凸的基础上,讨论了一类非线性分式规划问题的最优性条件和对偶,获得了Kuhn-Tucker最优性充分条件及对偶问题的弱对偶结果。
4) Kuhn-Tucker condition
Kuhn-Tucker条件
1.
In the framework of locally convex topological vector space,the scalarization theorem,Kuhn-Tucker conditions as well as the duality theorem and the saddle points theorem on Henig proper efficient solutions with respect to the base for vector optimization involving arcwise connected convex maps are established separately.
在局部凸拓扑向量空间中,建立了弧连通凸映射向量优化问题关于基的Henig真有效解的标量化定理、Kuhn-Tucker条件、对偶性定理以及鞍点定理。
2.
In our algorithm,replacing the lower level problem by its Kuhn-Tucker condition,the bilevel linear programming is transformed into a traditional single-level programming problem,which can be transformed into a series of linear programming problem.
在该方法中,用下层的Kuhn-Tucker条件代替下层问题,将原二层线性规划转化为传统的单层规划问题。
3.
Via connecting linear plus power module ideal point algorithm under Kuhn-Tucker condition,the bilevel multiobjective programming problem is changed to a singula.
给出双层多目标决策问题数学模型的一种解决方法,把线性加权模理想点法和Kuhn-Tucker条件结合起来,从而把双层多目标规划问题转化为单层单目标约束规划问题,进而求得原问题的满意有效解。
5) Kuhn Tucker condition
Kuhn-Tucker条件
1.
As for weak efficient solution to multi objective programming inequality and equality constrants, the new necessary condition between Fritz John condition and Kuhn Tucker condition is established under weaker condition.
针对具有等式和不等式约束的多目标规划的弱有效解 ,在相对较弱的条件下给出了一个介于著名的Fritz-John条件与 Kuhn-Tucker条件之间新的必要条
6) kuhn-Tucker conditions
Kuhn-Tucker条件
1.
The author has proved Fritz John conditions and Kuhn-Tucker conditions ofα-major optimal constraint solutions on the bases of the representation ofα-major constraint structure set for the problem.
在给出问题的α-较多约束集结构表示的基础上,证明了这类问题的α-较多约束最优解要满足的FritzJohn条件和Kuhn-Tucker条件。
2.
In this algorithm,inequality constrained least-square problems are first translated to convex quadratic programming problems and then translated to the linear complementarity problem(LCP) using Kuhn-Tucker conditions of quadratic programming,which consequently gives the general form of least-squares estimation in adjustment model,as well as the algorithm is simple and easy to understand.
采用的方法是先将参数带有不等式约束的最小二乘问题转换成凸二次规划问题,然后利用二次规划的Kuhn-Tucker条件把二次规划问题转换成线性互补问题(LCP),从而求得参数最小二乘估计的一般形式,并给出算法,便于在实际测量中应用。
补充资料：必要和充分条件
必要和充分条件
necessary and sufficient conditions
必要和充分条件〔。日沈，刃叮扣日，击da吐口侧如此;Heo6-xo四阳M从el.加cT.T。，.“eyc加皿，} 使得命题A成立的一些条件:当不满足这些条件时命题A不能成立(必要条件)，当满足这些条件时命题A必定成立(充分条件).必要和充分条件往往用短语“当且仅当”来代替.必要和充分条件具有重要意义.在一些复杂的数学问题中，寻找便于应用的必要和充分条件有时是很困难的.在这种情况下，人们便试图寻找较宽的充分条件，其中包含可能较多的条件，而所研究的事实仍然成立，以及较窄的必要条件，即其中包含可能较少的条件，使得所研究的事实不再成立.这样，充分条件逐步接近必要条件. E〔3.3张鸿林译
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