最小化

Keywords Closed convex cone;gradient projection method;Least-squares solution;Inverse matrix problem;Inverse eigenvalue problem;Matrix completion problem;Optimal approximation

Article From 湖南大学；应用数学博士论文 2005年度闭凸锥；投影梯度法；最小二乘解；矩阵反问题；矩阵逆特征值问题；矩阵完全化；最佳逼近

This property is independent with the convexity of the objective function and the line search used.

本文在此基础上利用后退线性搜索，提出一种解非线性最小二乘问题的结构化MBFGS公式。

This paper proposed to use elliptical Gabor filter with least redundancy to convolute with palmprint,sub-bands with 4 scales and 6 directions are obtained,calculate the average and deviation of every sub-band,48D texture feature is extracted,and normalize the 48D feature in the whole database,finally use distance of absolute value to measure the difference between two feature vector.The result shows the arithmetic proposed by this paper has a little high retrieval accuracy.

本文采用最小冗余度的椭圆Gabor滤波器组对掌纹图像滤波，得到4个尺度6个方向的子带，计算每个子带的均值与方差，得到48维的纹理特征，在整个数据库中对48维特征进行归一化，最后采用绝对值距离衡量不同特征向量间的差异。

School of Electronic and Information Engineering,Dalian University of Technology,Dalian,Liaoning 116024,ChinaStable processes can better model the impulsive random signals and noises in physical observation.This paper briefly describes its spectral representation,proposes a new different spectral density from power spectrum density of second order processes,thus can get a new concept of stable white noise based on covariation spectrum,and a method of identification of nonlinear PAR system based on least p-norm.

描述了稳定分布的谱表示，提出了共变谱密度的概念，得到一种基于自共变序列与共变谱的稳定分布白噪声与有色噪声的概念及其判断标准，对传统意义上的白噪声进行了广义化，依据多项式自回归系统模型，对基于稳定白噪声输入的系统输出非线性稳定有色噪声建立其非线性PAR模型，提出基于最小P范数的EIRLP算法对非线性PAR系统进行辨识。

Moreover, when the normalized damping matrix is diagonally dominant, it is strictly shown that decoupling the modal equations by neglecting the off-diagonal elements indeed minimizes the error upper bound.

同时，还严格地证明了，当正则化的模态阻尼矩阵是对角占优时，由忽略其非对角线元素使模态方程解耦的方法所引起的误差的上限的确能达到最小。

The initialized parameters of neural networks are selected, which is directed by rough set theory, and the networks are trained by using a probability-based BP algorithm, which minimizes system errors.

首先，利用粗糙集理论对神经网络初始化参数的选择和确定进行指导，赋予各参数相关的物理意义；然后，以系统输出误差最小化为目标对粗糙神经网络进行训练，使其满足性能要求。

It has unique substrate specificity, and required minimal sugar chain in the degradation direction and synthesis direction of trisaccharide and disaccharide separately.

该酶具有独特的底物特异性，其降解方向和合成方向所需的最小糖链长度分别为三糖和二糖，均比普通的葡聚糖磷酸化酶少一个糖基以上。

Using the convex set model to describe the uncertainty existed in the parts design.By adopting the physical planning method to construct discontentedness function of the uncertainty parameters.

用凸集模型描述零件设计中存在的不确定性，采用物理规划方法构造不确定性参数的不满意度函数，通过极小化不满意度函数最差值实现目标函数的稳健性，通过灵敏度分析实现约束函数的稳健性。

The first part is involved in the principles and algorithms on minimal disjoint sum of products of the system reliability structure functions, The second part is involved in the research on system reliability models and event-sequence analysis of large complex repairable systems.

论文分为两部分，第一部分是关于系统可靠性结构函数最小不交化的原理及算法的研究；第二部分是关于大型复杂可修复系统的可靠性分析模型及事件序列分析方法的研究。

For the problems to minimize the sum of earliness penalties and resource constrained problems, the optimal algorithms are given.

对目标函数为极小化提前惩罚和问题和资源约束问题给出了最优算法。

As she looked at Warrington's manly face, and dark, melancholy eyes, she had settled in her mind that he must have been the victim of an unhappy attachment.

每逢看到沃林顿那刚毅的脸，那乌黑、忧郁的眼睛，她便会相信，他一定作过不幸的爱情的受害者。

Maybe they'll disappear into a pothole.

也许他们将在壶穴里消失