但这种办法并不普遍，只能用于二元函数，来判断是极小值点、极大值点还是鞍点。
I should say that is for a function of two variables to try to decide whether a given critical point is a minimum, a maximum or a saddle point.
其中一个是找出一个函数的极小值，极大值，这个函数的变量是相关的，这种方法称为拉格朗日乘数法。
One of them is to find the minimum of a maximum of a function when the variables are not independent, and that is the method of Lagrange multipliers.
如果想知道是极大值还是极小值，那就只需用常识，或者直接比较各点的函数值？
So, if you want to know if something is a maximum or a minimum, you just have to use common sense or compare the values of a function at the various points you found. Yes?
在微积分中，在函数的极小值点上导数等于零或者不存在导数。
In calculus, the derivative equals zero or does not exist at a function's minimum point.
如果罚问题的极小点是原约束规划问题的极小点，则称此罚问题中的罚函数为精确罚函数。
If each minimum of the penalty problem is a minimum of the primal constrained programming problem, then the corresponding penalty function is called exact penalty function.
关于算法分析的定理证明了这种混合算法对于紧致集内的权向量构成的任意连续函数能依概率1收敛于全局极小值。
It is shown that this algorithm ensures convergence to a global minimum with probability 1in a compact region of a weight vector space.
CHNN的设计应保证，无论从何种初值出发，网络总能通过运行收敛到一个稳定状态，它相应于能量函数的某个局部极小点。
The design of CHNN should ensure that the networks always converge to a steady sate corresponding to a local minimum point of energy function by running in spite of starting from any initial values.
考虑当目标函数在约束条件下的最优值作扰动时，使各约束作极小扰动的非线性规划问题。
The nonlinear programming problem that the constraint perturbation attains minimum under the condition when the objective function makes its optimal perturbation is considered.
本文通过使用向量似变分不等式和半预不变凸函数来证明约束向量优化的弱极小值的存在性。
In this paper, We prove the existence of a weak minimum for constrained vector optimization problem by making use of vector variational-like inequality and semi-preinvex functions.
最大能量法的结果受初始静校正量的影响，它的解容易陷入目标函数的局部极小值。
The result of maximum energy method depends on the initial values of residual statics. The solution is often trapped into the local minimum of the objective function.
修改分割函数，使其仅在前景和后景标记位置有极小值。
Modify the segmentation function so that it only has minima at the foreground and background marker locations.
新算法选择很广一类的隐层神经元函数，可以直接求得全局最小点，不存在BP算法的局部极小、收敛速度慢等问题。
The algorithm can get global minimum easily with a wide variety of functions of hidden neurons, and no problems such as local minima and slow rate of convergence are suffered like BP algorithm.
极小极大原理论述的是函数的极小极大值与极大极小值之间的关系。
Minimax principle deals with the relation between the minimax value and maximin value of a function.
提出了一类解极小极大问题的熵函数法，这种方法也可用来解线性或约束优化问题。
A method for solving minimax problem is presented, which also can be used to solve linear or constrained optimization problems.
对于传统BP算法存在的收敛速度慢和易陷入局部极小值问题，人们提出了径向基函数网络。
People put forward radial basis function networks considering the conventional BP algorithm problems of slow convergence speed and easily getting into local dinky value.
在第8章，我们将讨论两个函数极小极大不等式及其对变分不等式和不动点理论的应用。
In Section 8, we shall discuss two-function minimax inequalities and their applications to variational inequalities and to fixed-point theory.
在此基础上利用流函数建立了变形区速度场，并利用计算机对变形能进行求极小值，得到了变形区的速度分布及拉拔力。
Based on the assumption, the computer was used to calculate the minimum deformation energy, and the speed distribution in the deformed area and the drawing force were gotten.
由于目标函数中存在大量局部极小点，在处理合成数据和实际数据时，该方法效果很差。
Because there are many local minimum points in objective function waveform inversion's effectiveness is weak when processing anamorphic data and actual data.
如果这个值小于或等于所有其它的函数值，那它就是绝对极小值。
If the value is less than or equal to all other function values, it is an absolute minimum.
该文首先给出了求在线性约束下极小化有限个阶梯函数和的一种分枝定界算法。
This paper first presents a branch-and-bound algorithm to minimize a finite sum of stair-case functions under linear constraints.
建模实践表明，改进后的BP算法可能使网络误差函数达到局部极小点，提高了算法的拟合精度。
Applying improved BP algorithm, it shows the improved BP algorithm can easily converge into the local minimum point and it can improve the accuracy of model.
基于对问题的分析，证明了这一问题等价于单机调度中极小化类似的延迟量函数。
Through the analysis of the problem, it is proved that the problem is equivalent to a single-machine scheduling for minimizing an analogous function of delay.
由于安全系数的目标函数是非凸的、多变量的并且存在多个极小值，所以一般边坡最危险滑弧的搜索是困难的。
Because the objective function of the safety of factor is nonconvex, multi-variable, and existing many minimums, searching the most dangerous failure surface usually is difficult.
通过最小化能量方案极小化代价函数，同时通过定点交替迭代策略将非线性方程进行线性化处理，快速恢复图像。
The cost functions are minimized by alternate minimization scheme. The nonlinear equations are linear by fixed-point iteration scheme.
提出了一种改进的势场函数，并对改进势场函数的规划方法进行分析，发现该方法并不能完全解决局部极小问题。
The matters what leads to failure in the planning of traditional APF because of the local minimum problem is discussed, and an improved artificial potential method is proposed.
基态波函数可以表示为沿这条确定轨迹的一系列积分，而能量则可以用位势极小值处的一系列微分表示。
The ground state wave function can be expressed as a series of integrations along the trajectory and the energy as a series of differentials at the minimum of the potential.
极大极小问题是一类不可微优化问题，熵函数法是求解这类问题的一种有效算法。
Minimax problem is a sort of non-differentiable optimization problem and the entropy function method provides a efficient approach to solve such kind of problems.
本文利用函数某处的各阶导数的特点，以确定函数在该处的单调、极大值、极小值、拐点及浙近线等。
With the features of a function's derivatives at a point, this paper discussed some problems of the function, such as monotonicity, local maximum, local minimum, inflection point, and asymptote.
针对粒子群优化算法(PSO)应用于多极值点函数易陷入局部极小值，提出旋转曲面变换(RST)方法。
Aimed at particle swarm optimization (PSO) algorithm being easily trapped into local minima value in multimodal function, a rotating surface transformation (RST) method was proposed.
针对粒子群优化算法(PSO)应用于多极值点函数易陷入局部极小值，提出旋转曲面变换(RST)方法。
Aimed at particle swarm optimization (PSO) algorithm being easily trapped into local minima value in multimodal function, a rotating surface transformation (RST) method was proposed.
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