拉格朗日乘子

From the perspective of the variational discussion of Lagrange\'s contributions to the principles and analyzation of mechanics,the interaction between the calculus of variations and mechanics,especially the variational principles is made clear.

结合拉格朗日微积分代数化方案和18世纪可积性条件的研究，探讨了拉格朗日关于变分法基础研究的数学背景及相关工作；通过对《分析力学》中静力学约束平衡问题的细致考察，系统探讨了变分法中乘子法则的力学渊源、提出过程及意义。

Under suitable assumptions, the relationship is established between the unconstrained minimization of the Hestenes-Powell augmented Lagrangian function on the space of problem variables and the solution of the original constrained problem, and a relationship is also presented between the unconstrained minimization of the Hestenes-Powell augmented Lagrangian function on the product space of problem variables and multipliers and the solution of the original constrained problem.

在适当的条件下，我们建立了Hestenes-Powell增广拉格朗日函数在原问题变量空间上的无约束极小与原约束问题的解之间的关系，并且也给出了Hestenes-Powell增广拉格朗日函数在原问题变量和乘子变量的积空间上的无约束极小与原约束问题的解之间的一个关系。

Systems of inqualities,the minimum or maximum of a convex function over a convex set,Lagrange multipliers,and minimax theorems are among the topic treated,as well as basic results about the structure of convex sets and continuity and differentiability of convex functions and saddle-functions.

其中对不等式系统、凸集上的凸函数的极小或极大、拉格朗日乘子和极小极大定理做了专题论述，同时对凸集的结构和连续性以及凸函数的可微性和鞍点函数的基本结果做了介绍。

The raw data of I, Q channels are converted into the same amplitude and phase data in polar coordinates. The formula of optimal bit allocation for the amplitude and phase is deduced by the Lagrange multiplier based on the Rate-Distortion equality.

将I， Q两路原始数据转化为极坐标下相同大小的幅度－相位数据，根据率失真不等式由拉格朗日乘子法推导了基于幅度微分熵和相位微分熵的最优比特分配公式，然后用对应的比特数分别进行幅度和相位的网格编码量化。

In chapter 2, the theory of an improved trilinear decomposition algorithm based on a lagrange operator has been described.

论文的第二章，提出利用拉格朗日乘子法的原理来构造目标函数的三线性分解改进算法基本思路。

By modifying the structure of transceiver, the complex computation of Lagrangian multiplier within traditional MMSE transceiver design can be effectively obviated, and thus the whole system complexity can be greatly reduced.

该方案通过对接收机的改进设计，能够有效地避免传统MMSE设计过程中出现的拉格朗日乘子不易计算的缺点，大大降低设计复杂度。

For each given slip surface, an optimization model is suggested combined with Lagrange multiplier method. Genetic algorithm is adopted to search for the key slip surface, and a fitness function is proposed.

对于每次搜索中给定的滑移面，结合拉格朗日乘子法提出边坡可靠度的计算模型；采用遗传算法搜索关键滑移面，提出边坡的适应度函数。

Compared with traditional method by solving a Jacobi matrix, calculating account is greatly decreased because only displacement and center of buoyancy need computing while those elements of waterline plane are not required.d Based on the research mentioned above, the paper presents the computer programmes of compartment definition, free surface effection, and some modules of the programme of the intact and damaged stability calculation.

与传统的拉格朗日乘子法相比，该优化方法公式推导简单，而且每次迭代只需计算水线面以下的排水体积和浮心坐标，不需计算水线面上的面积、漂心、惯性矩等要素，计算方法直接简便。 4在以上理论研究的基础上，开发了舱室定义，自由液面修正的计算机软件；编制了船舶完整、破损状态下的浮态、稳性计算的部分模块。

There is also a comprehensive treatment of optimality conditions, Lagrange multiplier theory, and duality theory.

这门课程也包括了对最优化条件，拉格朗日乘子理论，和对偶理论的综合论述。

In this paper, the Hestenes-Powell augmented Lagrangian function is again considered, for solving equality constrained problems via unconstrained minimization techniques.

在适当的条件下，我们建立了Hestenes-Powell 增广拉格朗日函数在原问题变量空间上的无约束极小与原约束问题的解之间的关系，并且也给出了Hestenes-Powell 增广拉格朗日函数在原问题变量和乘子变量的积空间上的无约束极小与原约束问题的解之间的一个关系。

For a big chunk of credit-card losses; the number of filings (and thus charge-off rates) would be rising again, whether

年美国个人破产法的一个改动使得破产登记急速下降，而后引起了信用卡大规模的亏损。

Eph. 4:23 And that you be renewed in the spirit of your mind

弗四23 而在你们心思的灵里得以更新