鞍点

本文进一步讨论ST分解，并把这种分解推广到广义鞍点问题上。

In this paper , we extend the ST decomposition to the generalized saddle point problem and present three block triangular preconditioners .

本文利用鞍点方程研究了具有功力学破缺和普通自发破缺的SU（2）L（？）

The chiral SU ( 2 ) _L ■ SU ( 2 ) _ ■ σ model with both spontaneous and dynamical breaking is investigated in terms of the saddle point equation .

多目标规划共轭对偶问题的Hα-鞍点定理

H_ α - Saddle Point Theorems in Conjugate Duality for Multiobjective Programming

齐n次（n为奇数）广义中心&细鞍点系统第11阶细鞍点量公式

Calculation Formula of Eleven-Order Weak Saddle Values in Generalized Center-Weak Focus System of Degree n

一类E（b，ρ）-凸半无限规划的对偶性及鞍点理论

Duality and saddle-point theory for a class of E_ ( b ,ρ) - convex semi-infinite programming

Lagrange泛函的鞍点的一个等价条件

An Equivalent Condition with the Saddle Point of Lagrange Functional

多目标半定规划的Lagrange对偶与鞍点定理

Lagrange Duality and Saddle Points Theorem for Multiobjective Semidefinite Programming

鞍点定理在Lagrange乘数法上的应用

Saddle Point Theorem and its Applications in the Method of Lagrange Multiplier

广义弱鞍点定理与Lagrange对偶；

Weak saddle point theorem and Lagrange duality ;

有效解的Lagrange乘子定理与鞍点理论

Match point hot point Lagrange multiplier theorem of efficient solution and saddle point theory

集-集映射向量极值问题的Lagrange乘子和鞍点定理

Lagrange Multiplier and Saddle Point Theorems of Vector Extreme Value Problem with Set-Set Maps

非完全Lagrange函数的鞍点条件

Saddle point conditon of incomplete Lagrange function

G-（F，ρ）凸性下的非光滑多目标分式规划弱广义Lagrange鞍点

Weak generalized Lagrange saddle point for the nonsmooth multiple objective fractional programming with g - ( f ,ρ) convexity

集值映射向量最优化的标量化、Lagrangian乘子与弱鞍点

Scalarization , Lagrangian Multipliers , and Weakly Saddle Points in Vector Optimization of Set-Valued Maps

新算法组合使用了层次分析法（AHP）中的标权转换法和内点法，将q个有效鞍点减少为一个。

Scale - weight transformation method in AHP and affine - scaling interior points algorithm reduced the number of efficient anchor points to one .

在鞍点近似下，建立了Z（N）互作用系统的生成泛函的一个普遍表述；

We work out a general formulation for the generating functional of Z ( N ) Gauge-Z ( M ) Higgs coupling systems in the Mean Field Approximation .

研究集值向量优化问题在标量集值Lagrange映射下鞍点的性质。

The properties of saddle-point for scalar set-valued Lagrange mapping in vector optimization ( problems ) with set-valued maps were studied .

Lagrangian对偶问题和鞍点最优性条件又是最优化问题中的重要课题。

The Lagrangian dual problem and the optimization conditions of the saddle point play important parts in optimization problem .

给出了齐次规划问题KKT点的一个等价性质，采用对约束函数k次方的方法得到齐次规划问题的一个局部鞍点。

When the object and constraint functions are continous , it shows the relations of KKT points and local saddle-points .

用鞍点平均场方法（到单圈修正）和强耦合展开技术，研究了非各向同性耦合Z（2）格点规范模型的相结构。

An unisotropic Z ( 2 ) lattice gauge model was studied by using the mean field method ( with one-loop correction ) and strong-coupling expansion technique .

Kirchhoff积分所需格林函数可以通过象征函数和鞍点法导出。

Green function that adapts to Kirchhoff integral method could be derived from symbol function and saddle point method .

然后，采用增广Lagrangian方法把这个单目标约束优化问题转化成一个存在鞍点的二人零和博弈问题；

Second the augmented Lagrangian method is taken to transform the constrained optimization problem into a zero-sum game with the saddle-point solution .

JK鞍点算法

JK Saddle Point Algorithm

在此无格点KMC方法中，使用了Dimer算法在势能面中搜索鞍点和低能盆底。

The saddle points and basins on the potential energy surface are tentatively located with the Dimer algorithm .

这种虚拟区域法通过引入Lagrange乘子使边界条件获得弱满足，从而构建相应的等价变分公式，由此导出的鞍点问题用共轭梯度法迭代求解。

We construct an equivalent variational formulation for the Dirichlet problem via introducing Lagrange multipliers , and the resulting saddle point problem is solved by the conjugate gradient algorithm .

在线性与非线性状态反馈控制共同作用下，在该系统原为鞍点的零平衡点上，创建了稳定的Hopf分岔行为。

The Hopf bifurcation behavior from the zero equilibrium , which is a saddle point , is created under the combination control of linear and nonlinear feedback .

e2跃迁是由于m1型和m2型鞍点能量简并引起的，沿着bz的∑和Δ轴方向。

E2 transition , which is due to the degenerate of M1-type and M2-type CPs , is expected to take place along Σ or Δ axis .

在此基础上，本文研究E-凸，半E-凸条件下的最优性条件、Lagrange乘子定理、鞍点定理，得到了很多很好的结论。这也是本文的主要工作。

Under the assumption of E-convexity and semi-E-convexity , the optimality conditions , Lagrange multipliers theorems , saddle points theorems are established , and these are primary in this thesis .

反应体系的代表点从山谷R沿反应途径爬过鞍点Q后落入另一山谷P中（R-Q-P线就代表反应途径）。

In the figure , the system will travel along the valley ( R ), over the saddle point ( Q ), and down into the second valley ( P ) . The reaction path is represented by R Q-P line .

接着重点讨论了Lagrange乘子的近似空间，即粘接元（mortarelements）空间的建立，以及所引起的离散鞍点问题的共轭梯度迭代解法。

Then we concentrate on the construction of the discrete space of Lagrange multiplier , the space of mortar elements , and the conjugated gradient method for the related saddle point problem .