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Third, this paper proposes a method of dealing with singularity of Jacobian matrix of robot manipulator, then introduces singular robust inverse matrix of Jacobian matrix.

并在拉格朗日—欧拉方程的基础上给出了机器人操作器的动力学方程，对动力学方程中的惯量项、重力载荷项进行了简化，并给出了哥氏力和离心力项的简单求法。

One day, when you descend into LaGrange from your space ship, you are attacked by mysterious robotic invaders.

有一天，当你陷入拉格朗日从您的飞船，你是神秘的机器人攻击入侵者。

This paper using trajectory planning based on spline function,rigid robot Lagrangian kinetics set up system mathematical model.

论文运用了基于插值样条函数的轨迹规划法，机器人手臂拉格朗日动力学方程建立了系统数学模型，为自动包装机机器人手臂系统设计提供了新思路。

The general algorithm steps based on subgradient optimization mathematics method are presented.

建立了这类问题的数学规划模型，并采用拉格朗日松弛算法对模型进行求解，给出了次梯度优化求解算法的一般步骤。

Computational examples show that the modified subgradient optimization algorithm for Lagrangean relaxation can reduce the iterative steps obviously, and is proved to be efficient.

算法实例表明，改进后的拉格朗日松弛算法迭代步数显著减少，证明算法是有效的。

In order to improve performances of computer communication networks, the important route selection optimization in computer communication networks is firstly studied in detail by using the modern metaheuristic search method, i. e., Tabu search, which is of great flexibility and came into use just a few years ago. Better results are obtained and compared with the traditional Lagrangean relaxation and subgradient optimization method. Especially, the superiority of this method over other algorithms is further shown in the case of very heavily loaded network. Thus, the new thinking and method are provided for the optimization theory of computer networks.

摘 要：为了改进计算机通信网络的性能，首次采用近年来才开始应用、且具有很强灵活性的现代超启发式搜索方法——Tabu搜索方法，对计算机通信网络中重要的路由选择优化问题进行了详细的研究，得到了比经典的拉格朗日松弛及子梯度优化方法更优的结果，尤其在网络负荷很重的情况下，与其它算法相比，更显示出该方法的优越性，从而为计算机网络的优化理论提供了新的思路和方法。

A lagrangian relaxation heuristic algorithm based on subgradient optimization is applicated to solving the practical scale problems. The solution algorithms solving sub-problems are also listed.

提出了求解实际规模问题的基于次梯度优化的拉格朗日松弛启发式算法，并给出了各子问题的求解算法。

In nowadays literature, schedule recovery problems are mainly modeled by time-space network, solved using Lagrangian relaxation heuristic algorithm, subgradient optimization and commercial optimization software ILOG.

目前国外主要采用时空网技术建模和拉格朗日启发式算法、次梯度优化法求解。

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。

The method of Lagrange multipliers can be used to reduce optimization problems with constraints to unconstrained optimization problems.

该方法的拉格朗日乘数可以用来减少优化问题与制约因素，无约束最优化问题。

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