正则参数求解的微分进化算法

研究了正则化方法中正则参数的求解问题,提出了利用微分进化算法获取正则参数.微分进化算法属于全局最优化算法,具有鲁棒性强、收敛速度快、计算精度高的优点.把正则参数的求解问题转化为非线性优化问题,通过保持在解空间不同区域中各个点的搜索,以最大的概率找到问题的全局最优解,同时还利用数值模拟将此方法与广义交叉原理、L-曲线准则、逆最优准则等进行了对比,数值模拟结果表明该方法具有一定的可行性和有效性.     

面向下一代光通信的VCSEL激光器仿真模型

根据L-I经验公式得到参数待定的L-I模型,并利用遗传算法搜索最优参数得到参数模型,对结果进行拟合优度检验,求出误差.在该模型基础上对环境温度进行修正并且考虑电流瞬时变化的影响,建立微分方程模型,采用Ode23求解,并利用遗传算法搜索最优参数得到参数,对结果进行拟合优度检验,得出了该激光器不同温度下的L-I特性曲线和激光器小信号幅频响应.同时根据速率方程推导出了带宽响应的数学模型,对参数归一化后,利用遗传算法搜索最优参数得到参数.     

总体最小二乘准则下非线性EV模型的参数拟合方法

在非线性回归模型参数拟合问题中,当数据中的每个变量都存在不可忽略的误差时,在普通的最小二乘准则下拟合出的参数不是最优的.按照总体最小二乘准则,以观测点到拟合曲线或拟合曲面垂直距离平方和为目标函数,然后用最优化方法搜索出使目标函数值取最小值的参数和数据点估计,从而给出求最优模型参数的算法,最后,通过计算机仿真和与文献比较,验证了提出方法的正确性.     

浅析有条件的分式化简与求值问题

解有条件的分式化简与求值问题时,既要瞄准目标,又要抓住条件;既要根据目标变换条件,又要依据条件来调整目标,常常用到如下解题技巧.1引入参数法此法的运用特点是当题目所给条件为连比等式的形式时,采用引入参数法进行转换.例1已知a2+b=b-32c=3c4-a,求5a8+a6+b9-b7c的值.分析审视条件和待求式,设连比值为k,则a,b,c分别能用参数k的倍数来表示,问题可迎刃而解.解设a2+b=b-32c=3c4-a=k,则a+b=2k,b-2c=3k,3c-a=4k,三式联立解方程组,得a=-151k,b=215k,c=35k.所以,5a+6b-7c8a+9b=5×(-115k)+6×251k-7×35k8×(-151k)+9×251k=15001.点评通过引入参数k,将条件转化为方程组,然后用k分别表示a,b,c,代入分式中求解.通过引入参数,实现将多元(a,b,c)转变为一元(k)来求解,既有条不紊又方便快捷.例2已知abc≠0,且a+cb=ba+c=c+ba,求(a+b)(b+c)(c+a)abc的值.分析审视条件和待求式,设连比值为k,则待求式等于k3,若能求出k,问题获解.解设a+cb=ba+c=c...     

多重因素约束下的网格搜索对策问题研究

首次基于搜索成本及搜索资源等限制因素,构造局中人面向多重约束条件的可行策略集合,建立相应的搜索空间;在给定搜索点权值的基础上,考虑搜索成本与搜索成功概率等因素,构造相应的支付函数,建立多重因素约束下的网格搜索对策模型.为简化模型求解,将对策论问题转化为约束最优化问题,求解约束问题获得最优值,转化为模型的对策值,并给出双方最优混合策略.最后,给出军事想定实例,说明上述模型的实用性及方法的有效性.     

我解这道竞赛题

2008年全国高中数学联赛吉林省预赛最后一题为:正数a,b,c满足:2a+4b+7c≤2abc,求a+b+c的最小值。此题的难度非常大,如何来求解呢?下面是笔者解此题时的一些思路,现整理出来供参考。注意到a,b,c是正数,利用均值不等     

用化归思想解高考题

<正>2014年高考数学(浙江卷)文科第16题:已知实数a,b,c满足a+b+c=0,a2+b2+c2=1,则a的最大值是__.分析本题主要考查最值求解的基本策略,咋看题目涉及到的字母参数较多,思路不太清晰,同学们很容易迷失方向以致半途而废.若把要求的字母a看作常量,其他字母如b和c看作变量,将题目条件化归为解析几何或方程或函数或三角函数或不等式或平面向量或     

关于∑(a/(b c))~(1/2)的上界

设△ ABC的三边长为 a、b、c,则有∑ ab c>2 ,其中 2是最佳的 .本文将讨论 ∑ ab c的最佳上界 .定理　在△ ABC中 ,有∑ ab c<2 33 1 ,( * )且 2 33 1是最佳的 .证明　 ( * )式关于 a、b、c完全对称式不等式 ,故设 c =1 ,a≥ b≥ 1 ,a 相似文献   

机器学习中的最优化模型与对偶

数学最优化是以数学的方式来刻画和找出问题最优解的一门学科.机器学习利用数据构造预测方法,并对这些方法进行研究.介绍了机器学习中与支持向量机和稀疏重构相关的最优化模型.在此基础上,给出了三个典型最优化模型的对偶问题,并详细地讨论了对偶在求解这些问题中的应用.     

一类双重最值问题的简解

文[1]通过三道数学竞赛试题总结出一类多变量双重最值问题的求解策略,但解法略显繁琐.笔者运用整体思想,给出此类问题的简证如下:例1设a,b,c∈R,且a+b+c=1,求min{max(a+b,b+c,c+a}}的值.(2001年北京市高中数学竞赛题)     

一种Logistic模型参数估计的新方法及应用

介绍了logistic曲线参数估计的一种新方法,它是利用三次样条插值函数求导代替logistic曲线在这一点的导数值,进而利用最小二乘法得出参数的估计值,通过实例分析表明本文提出的方法比一般的三点法估计的参数值k再用线性化方法估计的参数值b,c,拟合精度更高.     

Logistic曲线拟合方法研究

Logistic模型具有广泛的实用性。本文推导了用三点法估计该模型中参数K值的公式 ,并提出了估计K值的新方法一四点法和拐点法。用 3种方法求出K值后 ,再用线性化回归获得另外两个参数a、r,应用实例研究表明 :3种方法都可得到较高拟合精度 ,其中以四点法最优。而且 ,以这些方法得到的参数估计值作为初始值进行非线性回归 ,易获得 3个参数的最优估计。     

Point-based methods for estimating the length of a parametric curve

This paper studies a general method for estimating the length of a parametric curve using only samples of points. We show that by making a special choice of points, namely the Gauss–Lobatto nodes, we get higher orders of approximation, similar to the behaviour of Gauss quadrature, and we derive some explicit examples.     

基于CSO-SVR的气膜钢筋混凝土储仓主体结构施工成本预测研究

为了较准确的预测气膜钢筋混凝土储仓主体结构施工成本,提出一种鸡群算法(CSO)和支持向量回归机(SVR)结合模型,即CSO-SVR,利用CSO算法对SVR进行寻优得到全局最优解,从而得到具有最佳参数的支持向量回归机模型,通过气膜钢筋混凝土储仓主体结构施工成本数据预测仿真,结果显示:CSO-SVR模型预测精度高于PSO-SVR,GA-SVR,SVR,BPNN等方法,是预测气膜钢筋混凝土储仓主体结构施工成本的有效工具.     

A nonlinear time series model and estimation of missing observations

This paper formulates a nonlinear time series model which encompasses several standard nonlinear models for time series as special cases. It also offers two methods for estimating missing observations, one using prediction and fixed point smoothing algorithms and the other using optimal estimating equation theory. Recursive estimation of missing observations in an autoregressive conditionally heteroscedastic (ARCH) model and the estimation of missing observations in a linear time series model are shown to be special cases. Construction of optimal estimates of missing observations using estimating equation theory is discussed and applied to some nonlinear models.Authors were supported in part by a grant from the Natural Sciences and Engineering Research Council of Canada.     

球面上的几何连续插值

In this paper, a new method for geometrically continuous interpolation in spheres is proposed. The method is entirely based on the spherical B′ezier curves defined by the generalized de Casteljau algorithm. Firstly we compute the tangent directions and curvature vectors at the endpoints of a spherical B′ezier curve. Then, based on the above results, we design a piecewise spherical B′ezier curve with G 1 and G 2 continuity. In order to get the optimal piecewise curve according to two different criteria, we also give a constructive method to determine the shape parameters of the curve. According to the method, any given spherical points can be directly interpolated in the sphere. Experimental results also demonstrate that the method performs well both in uniform speed and magnitude of covariant acceleration.     

Plans dʼexpérience pour lʼestimation de la courbe de concentration et de lʼAUC

The problem of interest is to estimate the concentration curve and the area under the curve (AUC) by estimating the parameters of a linear regression model with autocorrelated error process. We introduce a simple linear nonparametric unbiased estimator of the concentration curve and the AUC. We show that this estimator constructed from an appropriate regular sampling design is asymptotically optimal.     

Successive direction extraction for estimating the central subspace in a multiple-index regression

In this paper we propose a dimension reduction method for estimating the directions in a multiple-index regression based on information extraction. This extends the recent work of Yin and Cook [X. Yin, R.D. Cook, Direction estimation in single-index regression, Biometrika 92 (2005) 371-384] who introduced the method and used it to estimate the direction in a single-index regression. While a formal extension seems conceptually straightforward, there is a fundamentally new aspect of our extension: We are able to show that, under the assumption of elliptical predictors, the estimation of multiple-index regressions can be decomposed into successive single-index estimation problems. This significantly reduces the computational complexity, because the nonparametric procedure involves only a one-dimensional search at each stage. In addition, we developed a permutation test to assist in estimating the dimension of a multiple-index regression.     

On Hsu's theorem in multivariate regression

The paper deals with optimal quadratic unbiased estimation of the unknown dispersion matrix in multivariate regression models without assuming normality of the errors. We show that Hsu's theorem for univariate regression models continues to multivariate models with no additional assumptions. Furthermore optimal quadratic plus linear estimating functions for regression coefficients are considered, and we investigate whether the ordinary linear estimates are the best. This leads to a new theorem which is similar to that of Hsu.     

Estimation for regression with infinite variance errors

This paper addresses the problem of modelling time series with nonstationarity from a finite number of observations. Problems encountered with the time varying parameters in regression type models led to the smoothing techniques. The smoothing methods basically rely on the finiteness of the error variance, and thus, when this requirement fails, particularly when the error distribution is heavy tailed, the existing smoothing methods due to [1], are no longer optimal. In this paper, we propose a penalized minimum dispersion method for time varying parameter estimation when a regression model generated by an infinite variance stable process with characteristic exponent α ε (1, 2). Recursive estimates are evaluated and it is shown that these estimates for a nonstationary process with normal errors is a special case.