英语语法分析

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。

The notions of subgradient, subdifferential, differential with respect to convex fuzzy mappings are investigated, which provides the basis of the theory of fuzzy extremum problems.

最后对凸模糊映射的次梯度、次微分和微分等概念进行了研究，为模糊极值理论打下了基础。

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.

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。