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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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