| 1. | Derivatives in higher dimensions , directional derivative and gradient
多维微分、方向导数和梯度。 |
| 2. | Derivatives in higher dimensions , directional derivative and gradient
在多维度中的微分、方向导数和梯度。 |
| 3. | Error estimates of directional derivatives of approximately specified functions
近似已知函数方向导数的误差估计 |
| 4. | We discuss several different definitions of directional derivative and gradient vector
摘要讨论了几种不同的方向导数和梯度的定义。 |
| 5. | Secondly , the new generalized gradient is introduced to take advantage of the given directional derivative
其次讨论了一类新的广义梯度，这样的广义梯度能够充分利用已经有的方向导数的信息。 |
| 6. | As the directional derivative defined in this paper does n ' t show convexity , when its properties are considered , it is necessary to search for new ways to reach the conclusion
本文定义的广义方向导数在一般情况下不具有凸性，因而研究其性质时，要采用新的方法来得到类似的结论。 |
| 7. | Used perturbed method and making inexact generalized gradient projection with cone , perturbed generalized gradient projection method is proposed . the field of the algorithm is extended . numerical experiments show that the method is effective . secondly , using the trust region form and the pseudo - directional derivative of minimax problem , we propose the trust region form of minimax problem
对信赖域法作了进一步的研究，借助minimax问题的伪方向导数，构造出其信赖域二次模型，并结合非单调策略，给出求解minimax问题的简单易行的信赖域算法。 |
| 8. | Section 3 and section 4 are the main parts of the paper . by employing the directional derivative and generalized gradient in the broad sense , as defined in this paper , the first order necessary condition and the first order sufficient condition of the single - objective non - smooth programming where the objective function is d - regular weak lipschitz function and constrained functions are regular weak lipschitz functions
第三节和第四节是本文的主要章节，以本文定义的广义方向导数和广义梯度为分析工具，对目标函数为d正则弱l函数，约束函数为正则弱l函数的单目标非光滑规划分别给出了一阶必要条件和一阶充分条件。 |
| 9. | Finally , this thesis discussed these following questions : first , the algorithm of used the error image for improving the purpose of the edge detection . secondly , we have transformed the solved question of the first and the second directional derivative to frequency domain and founded they have a single formulae in frequency domain . thirdly , we have described the singular signal and the noise by using the correlations of the neighbor data after wavelet transform
最后，在传统的边缘检测算法和小波分析的边缘检测算法之外，对以下几个方面也进行了一些讨论： 1 )利用误差图像来提高边缘检测效果的算法； 2 )将求解任意方向的一阶、二阶方向导数的问题转换到频域中去求解，发现在频域中它们具有简单易用的公式，使得原来求解任意方向的一阶、二阶导数的比较困难的问题变得容易实现了。 |
| 10. | Let / be a function from rn to r . following the definitions of the generalized gradients proposed by clarke and xu yihong , respectively , we define the d - regular weak lipschitz function and propose a new generalized gradient as follows where d _ f ( x ; d ) is the directional derivative of / in the direction d at the point x , namely some properties are proposed
第二节引入基本定义和记号，在clarke和徐义红提出的各自的广义梯度的基础上，定义了一类d正则弱l函数，且提出了一个新的广义梯度。设f ： r ~ n r ，其广义梯度为其中为f在处沿方向d的方向导数，即并给出了若干性质定理。 |
