极小值问题

How to deal with the restrictions of deep excavation is a very difficult problem. This paper analyzes the restrictions of pile-support structure detailedly, uses a castigatory function to deal with the restrictions, and adds the castigation to the function. Now the problem has changed to solve a minimal problem, and GA can be used to the optimal design successfully.

束条件的处理是遗传算法应用到深基坑支护结构优化的难题和重点，本文详细分析了桩撑支护结构的约束条件，采用了罚函数法对约束条件进行处理并反映到适应度函数上，使其变为无约束的极小值问题，从而使遗传算法得以顺利实施。

Based on the theory of isomorphic mapping and singular value decomposition theorem, the maximum of the kernel Fisher discrimination criterion can be skillfully acquired by solving the minimum of its reciprocal in a small space, and the final solution is acquired without taking account of the null space and non-null space of the kernel within-class scatter matrices separately.

基于同构映射原理和奇异值分解定理，在一个更小的空间内将核Fisher描述准则函数的极大值问题转化为其倒数的极小值问题，使最终的解不需要分开考虑核类内散度矩阵的零空间和非零空间。

For the single objective optimization, the decomposition and coordination method is adopted to build the decomposition and coordination model according to the existing sub-area division conditions of power networks. Then using the Augmented Lagrange method, the minimization problem of decomposition and coordination model can be changed to the saddle point problem of augmented Lagrangian function. Finally, the so called auxiliary problem principle is selected to decompose variables as well as the functions. This transforms the voltage and reactive optimization problem of the wholenetworks to some sub-problems in some sub-areas.

对于单目标无功电压优化，根据实际电网分区情况，采用分解协调法复制各分区的边界节点，建立分解协调模型，采用增广拉格朗日法将求分解协调模型的极小值问题转化为求增广拉格朗日函数的鞍点问题，然后采用辅助问题原理分解变量和增广拉格朗日函数，从而将全网无功电压优化问题分解为多个分区的分布式并行优化问题。

In this process, the main problems to be solved are initial configuration problem and local minimum problem.

在这个过程中所面对的主要问题就是初始结构的生成问题和局部极小值问题。

But this classical model has lots of shortcomings, including the local minimum problem.

但是，在实际应用中，这种经典的网络存在着诸多的缺陷，其中之一就是局部极小值问题。

This article discusses how to avoid local minima using additional momentum method with the help of MATLAB.

本文主要讨论在MATLAB下使用附加动量法使网络避免陷入局部极小值问题。

The problem control points of free-form surface are modified automatically can be reduced to the solution of energy functionals minimum under the condition of constraint.

将自由形状曲面的控制点自动修改问题归结为一个在约束条件下求解能量函数的极小值问题。

This paper proposes a learning algorithm of solving the local minimum problem and the un-learnable problem for the Hopfield neural networks.

本文针对Hopfield神经网络所存在的极小值问题及缺乏学习能力的问题，提出了一种学习算法。

Aiming at the difficulties of invalid solution and local minimum problems when traveling salesman problemis studied using Hopfield artificial neural network.

针对Hopfield神经网络在求解旅行商问题时出现的无效解和局部极小值问题，分析和比较两种改进的求解方法，首先从理论上证明算法的有效性，然后对两种算法分别进行计算机仿真，探讨网络收敛于全局有效解的途径。

Contrast source inversion algorithm recasts the inversion problem as a minimization of a cost functional, thus an iterative sequence is formed to reconstruct the contrast sources and contrasts.

对比源反演算法将反演问题转化为求解成本泛函的极小值问题，从而形成重构对比源和对比度的迭代序列。

Chrysanthemum of 10 thousand birthday is lax to edaphic requirement, with the arenaceous qualitative loam with fecund, good drainage had better.

万寿菊对土壤要求不严，以肥沃。排水良好的砂质壤土为好。

He unstepped the mast and furled the sail and tied it.

他拔下桅杆，把帆卷起，系住。