第五章，给出了解凸非线性半定规划的一种广义拉格朗日算法。
In the fifth chapter, we introduce an Augmented Lagrangian method for solving convex Nonlinear Semidefinite Programming (NLSDP) problems.
该算法利用拉格朗日算法将约束条件下的最优化问题进行转化，并采用对分算法加快搜索最优拉格朗日乘子的收敛速度。
Lagrange solution is employed to convert the constrained optimization problem and bisection method is used to reach a fast convergence in searching for the optimize Lagrange multiplier.
该算法使用了一种有效的表格查找和拉格朗日乘法器对分搜索办法，能够较快的收敛到最佳的功率点。
By means of the approach of look-up table and Lagrange? Multiplier bisect searching, this algorithm can be convergent to the optimal point of power rapidly.
为了解决多厂供应链生产计划的协调问题，提出了一种基于拉格朗日松弛算法的内部价格协调优化策略。
To solve coordination problem of multi-plants supply chain production planning, a coordination and optimization strategy of internal price based on Lagrange relaxation algorithm was presented.
ADAMS采用拉格朗日动力学方程，辅以刚性积分算法以及稀疏矩阵技术来求解模型。
ADAMS solves the model by adopting Lagrange dynamics equation and complementing with rigidity integral algorithm and sparse matrix technology.
提出在机群系统并行环境下的构造拉格朗日插值多项式的一种并行算法。
This paper presents a parallel algorithm for Lagrange's polynomial interpolation which is based on cluster parallel environment.
提出了一种基于数字微分和拉格朗日插值的系统频率快速而准确的测量算法。
An algorithm for power system frequency measurement based on numerical differentiation and central Lagrange interpolation is presented.
该算法充分利用拉格朗日松弛方法的特点，通过构建封闭图，对封闭图进行拉格朗日松弛求得满足条件的多播树。
The algorithm makes use of the characteristic of Lagrange relaxation method, and finds multicast tree satisfying constraint by constructing closure graph and making relaxation to this graph.
通过对模型的等价转换，设计了拉格朗日松弛启发式算法来求解模型。
Lagrange relaxation heuristic algorithm is designed to solve the model by equivalent transformation.
然后，运用凸优化技术分析了该资源分配问题，并基于拉格朗日对偶法给出了一种子载波和功率最优分配算法。
Then, by use of multiple carrier system's frequency-sharing property and convex optimization, a subcarrier and power optimal allocation algorithm is proposed based on Lagrangian duality theory.
通过对该算法及其改进算法以及拉格朗日松弛算法的应用效果分析，验证所提算法的有效性。
By the analyses of applications of the new algorithms and Lagrangian relaxation algorithm, the validity of the algorithms presented in this paper is verified.
随后，通过拉格朗日优化算法，找到了平衡编码量和失真大小的宏块的最佳编码模式。
Then we calculate the Lagrangian cost to balance the rate and distortion, by which we can find the best encoding mode.
采用椭球剖分策略剖分可行域为小的椭球，用投影次梯度算法解松弛二次规划问题的拉格朗日对偶问题，从而获得原问题的一个下界。
A projection subgradient algorithm for the Lagrangian dual problem of the relaxed quadratic problem is employed to general lower bounds of the optimal value for the original problem.
这种算法考虑了信源在量化器量化判决区域的分布，通过寻找最小的拉格朗日率失真费用函数，获得量化器的判决电平。
The source distribution in decision region of quantizer is considered in this algorithm, and the decision level of quantizer is derived from the procedure of searching the minimum R D Lagrangian cost.
但由于机组投运风险水平与机组强迫停运容量呈离散型的分布关系，因而难以与拉格朗日松弛法的机组组合算法有机结合。
However, the relation between unit commitment risk and forced outage capacity is a discrete distribution, the Lagrangian Relaxation unit commitment algorithm isn't used directly.
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。
Computational examples show that the modified subgradient optimization algorithm for Lagrangean relaxation can reduce the iterative steps obviously, and is proved to be efficient.
为了有效地求解该模型，提出了基于启发式的拉格朗日松弛分解算法。
To solve the model effectively, a Lagrange relaxation decomposition method with heuristic is developed.
针对问题的非凸性，提出了基于拉格朗日对偶方法的最优子信道、速率和功率分配算法，并从经济学的角度予以解释。
We formulated this optimization problem and solved it using the Lagrangian dual method and interpreted it from the angle of economics.
以医疗急救资源的配置问题为建模核心，运用次梯度最优算法对传统的拉格朗日松弛算法进行了改进。
This paper focuses on the modeling of the resources location of medical rescue. At first, the traditional Lagrangean relaxation algorithm is improved by using subgradient optimization algorithm.
演讲重点在分支介绍现代组合优化技术和减少算法和拉格朗日算符松弛接近。
The lectures introduce modern combinatorial optimization techniques, with an emphasis on branch and cut algorithms and Lagrangian relaxation approaches.
同时，论文提出的码率控制算法还对宏块层的率失真优化过程做了改进，根据每个宏块的预测目标比特数来调整率失真优化的拉格朗日系数，使帧层码率控制效果更优。
At the same time, this paper also improves the process of RDO in the macroblock layer. Based on the prediction bits of the macroblock, the Lagrange coefficient has been modified adaptively.
当位移和动量的拉格朗日多项式近似阶数满足一定条件时，可以自然导出保辛算法的不动点格式。
A fixed point iteration formula can be derived when the order of the approximate polynomials of displacements and momentum satisfy some certain conditions.
当位移和动量的拉格朗日多项式近似阶数满足一定条件时，可以自然导出保辛算法的不动点格式。
A fixed point iteration formula can be derived when the order of the approximate polynomials of displacements and momentum satisfy some certain conditions.
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