摘要李文学用拉格朗日函数提出求条件极值的充分条件，但他的证明却是错误的。
Wenxue li put forward a sufficient condition of conditional extreme value with Lagrange function but his proof is wrong.
摘要函数极值是应用数学解决实际问题的一个重要方面。
The function extreme value is an important aspect that applied maths solves the practical problem.
传统风煤比寻优通常采用求解燃烧函数解析式，再求极值得出最佳风煤比，这一方法可靠性差而且工作量大。
In traditional ways, the optimal air coal ratio is obtained by solving combustion function and finding out the extremum, which is time consuming and unreliable.
本文中，利用目标函数或约束条件的几何性质，提供了某些多元函数极值或最值问题的几何解法。
In the paper, it provides the geometrical solution to extreme value of many variables function by geometric properties of objective function or constraint condition.
本文给出调和函数极值原理的一种推广。
The note gives an extension of extremum principle for harmonic functions.
本研究所建立的冲线模式是依据多变数函数极值法与静力学力矩平衡原理设计而成。
The loom finish modeling in this research is designed according to the extreme of function and the statics moment balance theory.
这本书的目的是为了提供各类凸集和凸函数理论的介绍，它们在极值问题的应用中发挥核心作用。
The purpose of this book is to provide an exposition of the theory of convex sets and functions in which applications to extremum problems play the central role.
用特定系数法、换元法、配方法探求二元二次函数的极值公式。
The extremal formula of binary quadratic functions is studied by using method of undetermined coefficients, substitution method and method of completing the square.
研究一种多变量非线性函数极值的通用数值解法，并将这种算法应用于石英晶振热敏网络温度补偿系统中。
An universal numerical algorithm of extremum for multivariate nonlinear function is discussed, and is used in the calculate system of compensation for thermistor net.
同时，在具体反演中使用快速模拟退火算法，可以克服目标函数局部极值的限制，从而获得全局最优解。
Meanwhile, we use a fast simulation annealing algorithm in the inversion, which can overcome the limitation of the local extremum of objective function, and acquire a global optimum result.
对屈服条件与屈服函数的极值条件进行了讨论，在不需要流动法则的情况下建立了速度方程。
The extreme conditions of yield condition and yield function are discussed; and a velocity equation is established under the condition that no flow rule has been required.
判别函数极值的方法是数学分析中的重要组成部分。
Extreme function analysis of the mathematical method is the important component.
在很多实际问题中，会遇到求连续函数的极值问题。
In a lot of practical problems, one often encounters the extreme problem of continuous functions.
也是函数的极值、幂级数理论等众多数学理论的基础。
Is also a function of extreme value theory, and many other mathematical theory of power series basis.
微粒群优化算法是求解连续函数极值的一个有效方法。
Particle Swarm Optimization (PSO) algorithm is a powerful method to find the extremum of a continuous numerical function.
多峰值函数的极值问题一直是优化领域中的一个难点和热点。
Extremum problem of multimodal functions is a difficult issue in optimization fields.
利用二次型的理论，给出解决多元函数极值问题的另一种方法。
Through the quadratic form theory, another solution to the extremum problem of function of several variables is given.
经典的粒子群优化算法是一个在连续的定义域内搜索数值函数极值的很有效的方法。
The classical Particle swarm optimization (PSO) algorithm is a powerful method to find the minimum of a numerical function, on a continuous definition domain.
单叶函数的系数估计问题、极值问题研究一直倍受各国数学家高度关注。
The problems of coefficient estimates and extreme values of univalent functions are highly emphasized all the time by mathematicians from all over the world.
讨讼色泊松噪声驱动系统，利用统一色噪声近似方法，得到系统几率密度主方程，定态几率分布函数及其极值方程。
By using the unified colored noise approximation method, the master equation for probability density, the steady state probability distribution function and its extrema equation are derived.
本文使用二次型的理论进行判断，并将问题扩大为求任意多元函数的极值。
This paper USES the theory of quadratic form to distinguish this problem, not only that, it enlarge to calculate extreme value for function of many variable.
对“抢渡长江”问题进行了分析，建立了一种函数极值的数学模型，分析了解题思路和初等求解方法。
In this paper, the problem of Crossing Speedily the Changjiang River is analysed, and a type of functional extreme value model is built, then its analysis and elementary solution is illustrated.
以中值定理为工具，给出了利用一阶偏导数判定二元函数极值的方法。
The criterion extreme value of binary function for first partial derivative is given by means of the mean value theorem. The two theorems are obtained.
本文给出了利用梯度判定多元函数极值的判别法，并提供了若干范例。
In this paper we give a method of test, which makes use of the gradient, to verify the extreme value of multivariate function, and give some typical examples.
定理1设函数在处可导，且在处取得极值，那么。
Theorem 1 if is differentiable at, and is a local extreme value of, then.
针对多极值连续函数优化问题，提出了一种自适应蚁群算法。
An adaptive ant colony algorithm is presented for the optimization of multi-minimum continuous function.
通过对两类特殊三元函数极值问题的探讨，得到了由其系数来判别它们能否取得极值的充分条件。
Via the discussion about the extremum question of two kinds of special ternary function, Obtain the sufficient condition of judging if they can get the extremum by their coefficients.
通过对两类特殊三元函数极值问题的探讨，得到了由其系数来判别它们能否取得极值的充分条件。
Via the discussion about the extremum question of two kinds of special ternary function, Obtain the sufficient condition of judging if they can get the extremum by their coefficients.
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