拉格朗日函数

当将熵函数作为正则项加到拉格朗日函数上，我们得到了逐点逼近于M（x）的光滑函数。经证明，该函数即为指数罚函数。

When adding an entropy function as regularizing term to the Lagrangian function , we obtain a smooth approximate function for M ( x ) , which turns out to be the exponential penalty function .

极大熵方法是解有限极大极小问题的一种有效光滑化法，它通过在极大极小问题的拉格朗日函数上引进Shannon信息熵作正则项，给出一致逼近极大值函数的光滑函数。

Maximum Entropy Method is an effective smoothing one for the finite min-max problem , which , by adding Shannon 's informational entropy as a regularizing term to the Lagrangian function of min-max problem , yields a smooth function that uniformly approaches the non-smooth max-valued function .

推导给出该凸优化模型对应的拉格朗日函数及KKT条件，并引入凸优化内点法作为负荷分配的有效计算工具。

The interior-point method for convex optimization is presented here as a computationally efficient tool .

然后，运用条件极值和拉格朗日函数，针对在特定收益率下使风险达到最小的经济命题建立模型，并结合实例，利用MATLAB软件加以计算，得出最佳投资比例。

Then , with condition , extremum and Lagrange function aim at under specific yield to make risk reach minimum economic proposition to establish model . And combine example , calculate using MATLAB software and reach investment proportion .

同时，在算法中引入拟拉格朗日函数的概念，用有限差分法综合处理简约QP问题目标函数的一次项系数，进一步提高了优化计算效率和求解的可靠性。

With great efficiency and reliability , the resulted algorithm presents the definition of quasi Lagrange function and simultaneously deals with the first order term of reduced QP problem with finite difference approach .

应用Hamilton原理，找到引力场中自由粒子的拉格朗日函数，同时考虑史瓦西度规和拉格朗日方程，推导出行星绕太阳运动的轨道方程。

The Lagrange function of a free point in gravitational field is found by applying the Hamilton principle . Based on the Schwarzschild Gauge and the Lagrange equations , the moving orbital equation of the planets round the sun is derived .

谐变电磁场的拉格朗日函数及其变分问题

Lagrange function and variation fundamental for the harmonic electromagnetic field

非线性规划中的增广拉格朗日函数与近似最优解

Augmented Lagrangian function and approximate optimal solutions in nonlinear programming

建立机械手系统的拉格朗日函数；

Building the Lagrange function of the robot arm system ;

供水系统调度的增广拉格朗日函数优化方法

Augmented Lagrangian approach for optimal dispatch of water supply system

不等式约束优化问题的一个精确增广拉格朗日函数

An Exact Augmented Lagrangian Function for Nonlinear Programming Problems with Inequality Constraints

用拉格朗日函数研究谐振电路

A Study of the Resonance Circuit Through The Use of Lagrange Function

非线性规划的一类新增广拉格朗日函数

A new class of augmented Lagranian function for nonlinear programming

根据拉格朗日函数和哈密顿函数分析了产生电荷密度调制的关键因素，电子与声子的耦合以及磁场是产生电荷密度调制状态的关键因素。

Electron-phonon interactions and magnetic field were main factors producing charge density modulation .

修正的增广拉格朗日函数内点拟牛顿法

Interior-point Quasi-Newton Method of Modified Augmented Lagrangian Function

关于拉格朗日函数性质的讨论

Discussions on the properties of Lagrangian function

约束优化问题修正拉格朗日函数的鞍点与最优路径的收敛

On Saddle Point of Augmented Lagrangian for Constrained Optimization and the Convergence of the Optimal Path

这些质量来自于拉格朗日函数中，一般粒子与希格斯场的交互作用项。

The masses arise from the terms in the Lagrangian that have the particles interacting with the Higgs field .

第一章是本文的绪论部分，简要介绍了修正拉格朗日函数和本文的主要工作。

Chapter 1 is the introduction of this paper , which introduces the augmented Lagrangian function and the main results obtained in this paper .

加速参考系中的非线性完整系统，在空时坐标作无穷小变换下引起拉格朗日函数和约束方程的变化，导致了普遍的变换结果；

The change of Lagrange 's function and constraint equations of non-linear non-holonomic system in non-inertial system under the infinitesimal transformations of the time-space points leads to general transformation result .

采用拉格朗日函数与哈密顿量来讨论非惯性系统在有心力场存在时的运动方程。

In this paper , Lagrange function and a Hami quantity are used to develop the equation of motion for a non-inertial system in the presence of central force field .

算法首先构建包含比特和功率值的拉格朗日函数，对其求导，获得每个子载波的最佳比特功率值。

Firstly , the algorithm constructs Lagrange function containing bit and power values , then obtains the optimal bit and power values of each subcarrier by the differential of Lagrange function .

在恒定流的条件下，利用拉格朗日函数导出了推广的伯努利方程，从而说明了寻找的能量泛函的正确性。

That the extended Bernoullian equations can be derived from the Lagrangian function under the condition of the flow being steady , demonstrates that the energy functional presented in this paper is valid .

本文不用拉格朗日函数，而是直接通过消去一个变量将条件极值转化成无条件极值，重新推导出充分性条件。

This text derives out the sufficient condition again no using Lagrange function , but direct eliminating a variable from the side condition to transform conditional extreme value into the unconditional extreme value .

引入了拉格朗日函数，建立了温室气体排放权交易市场的模型，并进行了实证研究，得出了适合中国的配额机制。

Introducing the Lagrange function to set the emission rights trading model in greenhouse gases market and then make the empirical study to discuss the trend in the emission right in greenhouse gas market . 4 .

利用力学控制系统的仿射联络模型的内在几何齐次结构和李代数结构，研究了系统的短时间局部能控性，其中，系统的拉格朗日函数取为系统的动能。

Relying on the inherent geometric homogeneous and Lie algebraic structure for the affine connection model of mechanical control systems with kinetic energy Lagrangian , the small - time local controllability for the systems is explored .

在转动坐标系内，通过引入惯性力场及广义惯性势，拓宽了拉格朗日函数的内涵，导出了转动坐标系中的拉格朗日方程。

In the rotation coordinate system , through the introductions of inertia force field and the generalized inertia potential , This article opens up the Lagrange function connotation , derives Lagrange equation in the rotation coordinate system .

这种方法通过构造评价问题的最优化模型与拉格朗日函数，得出评价指标的客观权重，再利用权重合成公式，将主客观权重加以合成。另一种是熵权系数法。

For the former , by constructing a optimization model and Lagrange function , the objective weight of evaluation index is got , and by the weight combination formula , the subjective and objective weight are combined .

针对似水准椭球密度分布的合理性和稳定性问题，初步提出了求解似水准椭球的拉格朗日函数和哈密顿积分的设想。

In the light of the rationality and stability problem of density distribution of " quasi level ellipsoid ", we primarily put forward the idea to solve " quasi level ellipsoid " using Lagrange function and Hamilton integration .

在线性化增广拉格朗日函数法的基础上，利用双环迭代的思想，提出稳态递阶优化开环算法&增广开环关联平衡法。

This paper proposes an open-loop algorithm about the steady state hierarchical optimization , I , e. an augmented interaction balance method . It is obtained from basing on the linearized augmented lagrangian method and using the double loop iteration .