连续可微

精确罚函数又分为不可微精确罚函数和连续可微精确罚函数。

Exact penalty function is divided into nondifferentiable exact penalty function and continuously differentiable exact penalty function .

根据模型所有函数是否连续可微，可以分为光滑最优化和非光滑最优化。

According to the function is continuously differentiable or not , it is divided into smooth optimization or non-smooth optimization .

若目标函数连续可微，且其一阶导数Lipschitz连续，证明了并行拟牛顿算法的全局收敛性。

If the target function is continuously differential and Lipschitz continuous in first order derivative global convergence is demonstrated for the parallel pseudo-Newtonian algorithm .

此算法的突出特点是自然满足充分下降条件，在F是P0+R0的二次连续可微函数时，证明了算法的全局收敛性，文后的数值实验表明该算法具有潜力。

The distinguishing feature of the new method is that it satisfies sufficient descent condition naturally . Its global convergence is proved when F is P_0 + R_0 and quadratic continuous differentiate function . Numerical results are given which indicate that the method is efficient .

通过Fourier级数方法，得到时滞微分方程连续可微周期解存在的充要条件，同时为如何找周期提供了一个公式时间（英文）

By using Fourier 's series , the sufficient and necessary condition is obtained for periodic solutions to neutral time delay differential equations with variable coefficients and , in the meantime , a formula of evaluation of period is given , also .

通过引入非线性测度的概念，不要求激励函数连续可微、单调非降或有界，并假设自反馈项为非线性，研究了一类Hopfield神经网络平衡点的存在性、唯一性。

The existence , uniqueness of the equilibrium point of a class of Hopfield neural networks were studied by introducing nonlinear measures . The activation function is nonlinear and not necessary to be continuous , monotone and bounded .

首先利用压缩映象原理，结合一些先验估计式及Bessel函数的收敛性，根据KleinGordon方程初值问题的等价积分方程，在二次连续可微空间中得到了初值问题解的适定性；

Firstly , using the contraction mapping principle , combining some priori estimates and the convergence of Bessel function , the well_posedness of solutions of the initial value problem in twice continuous differentiable space was obtained according to the equivalent integral equation of initial value problem for the Klein_Gordon equations .

完全集上的连续可微函数的开拓

Extensions of Continuous Differentiable Functions Defined in Perfect Sets

多复变数连续可微函数的积分表示及其应用

The Integral Representation of Continuously Differentiable Function in Several Complex Variables and its Application

连续可微精确罚函数就克服了上述缺点，因此具有更好地性质。

Continuously differentiable exact penalty function overcomes the above shortcomings , it has better properties .

本文引进了连续可微和均匀连续可微两个新的可微性概念。

Two new notions of continuous differentiability and uniformly continuous differentiability are introduced in this paper .

无限次连续可微函数

Infinitely continuously derivable functio

一阶非线性椭园型方程组连续可微同胚解的存在定理

The Existence Theorems of Continuously Differentiable and Homeo - morphic Solutions for Nonlinear Elliptic Systems of First Order

仿真实验表明，该算法能准确、快速地找到连续可微多峰函数的全部极值点。

The experiments manifest that the hybrid algorithm can properly and quickly find all local optimization of the continuous-differential function .

本文完全用初等的方法证明了完全集上连续可微函数都有可微开拓。

By very elementary method , it is proved that every continuous differentiable function defined in a perfect set has differentiable extension .

讨论了一类多目标优化问题的区间斜率方法，其中目标函数是一阶连续可微的。

This paper describes the interval slope methods for a class of multiobjective optimization problems , of which the objective functions are in C1 .

终端约束的出现使得最优控制问题的值函数不仅仅不是连续可微的，甚至是不连续的。

The presence of an end-point constraint makes the value functions neither be continuously differentiable , nor be finite valued on the interior of its effective domain .

对通项为连续可微函数的函数列，给出了其有限和的精确积分表示；可用于任意精度要求的近似计算。

An exact integral expression of finite sum of sequence of a continuously differentiable function has been given , which can be used in approximate calculation with arbitrary accuracy .

证明了随机目标函数的每个样本函数是连续可微的凸函数，给出了选择随机最优场址的算法，并证明了其收敛性。

It is proved that the sample function of random objective function is continuous differentiable and convex . The algorithm for random continuous type optimal location is provided and its convergence is proved .

在被积函数是二次连续可微或二次分段连续可微的条件下，考虑了定积分近似计算的中点矩形法、梯形法和抛物线法，并且得到误差的最佳估计。

Approximately calculating definite integrals by midpoint-rectangular method , trapezoidal method and parabolic method are considered for the integrands which are twice continuously differentiable or twice piecewise continuously differentiable and the best estimations of errors are obtained .

传统以梯度为基础的最速下降法、线性规划、单纯形方法等优化方法，在问题的目标函数是凸集、连续可微可导等情况下，具有较高的计算效率。

Conventional optimization such as steepest descent method , linear programming , simplex method that method gradient-based have high computational efficiency when its objective function of the problem is such circumstances as convex , continuous and differentiable .

将这种方法应用到不同的函数类上，就可得到各种不同的具体的迭代公式。例如，应用到二次连续可微函数类上，就包含了[2]，[3]的结果；

For example , if we apply it to the double continuously differentiable function class and the continuous function class respectively , the results in [ 2 ] 、 [ 3 ] and [ 4 ] are derived .

而且经过证明，最优回收定价函数是初始库存之和的非增函数，最优值函数是库存状态变量的连续可微和联合凸函数。

It is proved that the optimal acquisition price is nonincreasing in the combined serviceable and returns inventories . Furthermore , the optimality value function is jointly convex and differentiable in the serviceable inventory and the returns inventory .

为不等式约束最优化问题提出一个连续可微近似罚函数并研究它的性质.在此基础上，提出了两个罚函数方法并证明这两个方法是全局收敛的。

In this paper , a approximate exact differential penalty function for optimization with inequality constraint is introduced and its properties are studied . As a result , two new penalty methods are proposed and the global convergence of the two methods is obtained .

Bush连续不可微函数的分形性质

The fractal properties of Bush continuous and non-differentiable function

一个七进位制小数定义的连续不可微函数的Hausdorff维数

Hausdorff Dimension of A Continuous and Non-differentiable Function Defined by Septenary Decimal

他首先讨论了其连续不可微函数的例子。

He first discussed his example of a continuous nondifferentiable function .

一个五进位制小数下的连续不可微函数及推广

An continuous and non-differentiable function defined by quinary decimal and extending

该方法对目标函数无连续、可微等要求，能较快地收敛到全局最优权系数。

Usually , the algorithm can quickly converge to the global optimum weight coefficients .

该算法具有强大的全局搜索性能和不要求目标函数连续、可微等特点。

This algorithm has a strong global - searching performance and has no requests for the continuity and differentiability of object function .