考虑了二次梯度项的非线性双重介质模型。
A nonlinear dual-porosity model considering a quadratic gradient term is presented.
此外，相应于次梯度算法的实现方式，提出两种分布协调结构。
In addition, two coordination frameworks were proposed corresponding to the two implementing ways of sub-gradient algorithm.
根据无约束最优化问题的梯度算法，提出了二次梯度算法，并证明了其收敛性。
In this paper, the gradient computational algorithm about unconditional extreme value is given.
考虑了二次梯度项影响的非线性径向流动问题的无限大地层和有界地层渗流模型。
The models of the nonlinear radial flow for the infinite and finite reservoirs including a quadratic gradient term were presented.
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。
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.
根据纹理位于图像中灰度突变处的特点，采用典型梯度算法，对目标图像进行两次梯度锐化。
According to the feature that the surface textures locate in the sudden change areas of image grey value, the double grade sharpening was performed for the image using the typical grad algorithm.
在非线性偏微分方程中，根据弱可压缩液体的假设，忽略二次梯度项，在试井较长时间内将产生误差。
According to the assumption of slightly compressible fluid, neglected the quadratic gradient term in nonlinear partial differential equation is usually lead to error.
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.
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.
文中给出了最优性条件、次梯度集合的构造方法及算法的迭代程序，提出了新的删除定理，可以减少迭代过程所储存的次梯度的信息量。
The subgradient set, optimization and procedure are constructed. In particular, a new deletion rule is suggested to reduce the amount of information to be stored during the computation procedure.
文中给出了最优性条件、次梯度集合的构造方法及算法的迭代程序，提出了新的删除定理，可以减少迭代过程所储存的次梯度的信息量。
The subgradient set, optimization and procedure are constructed. In particular, a new deletion rule is suggested to reduce the amount of information to be stored during the computation procedure.
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