方向导数

On the basic that existing second-order sufficient condition for an isolated minimizer of order 2 for unconstrained multi-objective optimization, using the so called oriented distance from a point to a set, l-stable function and generalized second-order Peano direction derivative, some second-order sufficient conditions for an isolated minimizer of order 2 for constrained multiobjective optimization problems with l-stable functions are obtained.

在已有的无约束l-稳定函数多目标优化问题的二阶充分条件的基础上，借助定向距离函数和l-稳定函数的性质及引入的广义二阶Peano方向导数，进一步刻画了具有抽象约束的l-稳定函数的多目标优化问题的二阶孤立极小点的二阶充分条件。

Furthermor, we consider their nondiferentiable situation, we define nonsmooth univex functions for Lipschitz functions by using Clarke generalized directional derivative and study nonsmooth multiobjective fractional programming with the new convexity. We establish generalized Karush-Kuhn-Tucker necessary and sufficient optimality condition and prove weak, strong and strict converse duality theorems for nonsmooth multiobjective fractional programming problems containing univex functions.

而且，本文利用Clarke广义方向导数针对Lipschitz函数在原来一致凸函数概念的基础上定义了不可微的一致凸函数，并利用这类新凸性，我们研究了非光滑多目标分式规划，获得了广义Karush-Kuhn-Tucher最优性条件；弱对偶定理、强对偶定理和严格逆对偶定理。

This study is the profile,gravity data to obtain Moho depth,gravity basement structure and depth distribution.

针对漠河盆地内的重力场资料特点和需要解决的地质问题，采用了下列常规处理技术：曲线的圆滑、方向导数的计算；同时，采用了DCT反演技术。

And the expression of its subdifferential is developed in the case that the effective domain of the optimal value function is a non-empty convex set.

最后利用方向导数和次微分导出了广义半无限极大极小规划的一个一阶最优性条件及其等价形式。

Stochastic convex programming; Monte Carlo methods; Financial optimization; Convergence with probability one; Optimality condition; Monte Carlo penalty function methods; Nonsmooth optimization; Directional derivative; Subdifferential; Confident interval; Conditional Value-at-Risk; Optimal reinsurance

基础科学，数学，运筹学随机凸规划； Monte Carlo方法；金融优化；以概率1收敛；最优性条件； Monte Carlo罚函数法；非光滑优化；方向导数；次微分；置信区间；条件风险价值；最优再保险

The extreme value of binary function at f_f_-f~2_=0 is judged by its direction derivative which follows ray starting from stable point and passing point P at every point P in noncentral neighborhood of stable point .

用驻点的去心邻域内各点P处函数沿以驻点为端点的过点P的射线方向的方向导数是否同号，来判定二元函数f在fxxfyy-f2xy=0时的极限。

Image is processed by using median filter and unsharp mask. The infrared image intensity surface is fitted by Haralickd discrete orthogonal polynomial basis function,and then the maximum points are detected on the fitted intensity surface by convolving the image with the second order directional derivative operators.

中文摘要：提出一种红外弱小多目标图像检测方法，图像先经过中值滤波、高提升滤波增强处理，再用基于Haralick离散正交多项式曲面拟合图像，拟合曲面的极大值点即目标点，可以利用导出的二阶方向导数算子与图像进行卷积得到。

With the development of highway construction, the speed of cars has been gradually increased.

随着公路的发展，汽车的车速也在不断提高。

So we basically had to develop a bond with the animal in terms of socializing with it.

所以我们就主要想通过跟它沟通的方式来建立一种良好的关系。