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1.
针对不同类别样本数差异和不同误分代价的分类问题,提出了一种基于最小二乘加权支持向量机的分类预测方法。在最小二乘加权支持向量机的基础上,考虑不同类别样本数差异和不同误分代价,提出了新的最小二乘加权支持向量机分类模型,构造了新的最优分类函数。将该模型应用于个人信用预测实验,与已有方法的对比实验结果表明,提出的模型在解决不同类别样本数差异和不同误分代价的个人信用预测问题时,有效地降低了总误分代价,提高了个人信用预测精确度。  相似文献   

2.
F-互补问题及其与极小元问题的等价性   总被引:11,自引:1,他引:10  
本文在Banach空间中引进了 F-互补问题,讨论了这一问题解的存在性,在向量格中,给出了F-互补问题的可行集是 ∧ -子格的条件,研究了F-互补问题与最小元问题的等价性。  相似文献   

3.
本文提出并讨论了最小费用流的反问题:如何在有限的投资条件下,最有效地扩充容量参数,达到一个予定的流值。建立了反问题的数学模型,给出了最优参数配置的算法。  相似文献   

4.
平面上的min-max型点-线选址问题   总被引:2,自引:0,他引:2  
本文研究两类平面选址问题:(1)求一直线到n个给定点的最大加权距离为最小;(2)求一点到n条给定直线的最大加权距离为最小.对这两个非线性优化问题,我们给出最优解的刻划及迭代次数为多项式的算法.  相似文献   

5.
多重整体谱范数最小摄动问题的可解性   总被引:1,自引:0,他引:1  
黄开斌  颜世建 《计算数学》1997,19(2):185-192
1.引言Golub和VanLoan等人[1-8]均研究了TLS问题或多重整体最小二乘问题(简称MTLS问题):的可解性,其中AECm×n,BECm×d.我们在[6,7]中给出了该问题可解的充要条件如下:定理.设(A,B)H(A,B)=Cdiag(Al,AZ,…,人十d)C”,其中》1>入2>…>人>人十1=…一入。+1=…一人t>人在十1三…三入n+d;s5fi<t5fi+d,CHC一人十d.记则MTLS问题(1.1)可解的充要条件是存在T的子集T’={if,iZ,…,i。n}使rank(屯…,c:。;cL;…;ex+。)=d·(1·2)有趣的是,我们发现存在矩阵对(人B)(见…  相似文献   

6.
证明了3-正则图的最小平分问题和最小α-分割问题都是NP-完全问题.  相似文献   

7.
基于偏最小二乘回归的美式期权仿真定价方法   总被引:7,自引:0,他引:7  
本文应用最优停止理论给出了美式期权定价的一般理论框架,进而给出了美式期权普通多项式偏最小二乘仿真定价算法.解决丁当前普通最小二乘方法的理论缺陷.最后以数字实验演示了无红利美式股票卖权的价值计算,实验结果表明该方法是可行的.  相似文献   

8.
1.引言我们将考虑具有退化系数的椭圆问题其中 Ω为 IR2中的一个凸多边形区域,定义为这里的g>0为分片线性连续函数.从物理背景来看,问题(1.1)来源于轴对称共振结构中的电磁场研究.Marini,Pietra(1995)[4]研究了问题(1.1)的混合有限元逼近,并得到了最优误差估计. 此文,我们采用一种新的混合元,即最小二乘混合元方法[5];对退化问题(1.1)进行逼近,利用插值投影证明了近似解具有最优阶精度的收敛性.比较起经典混合元方法来,最小二乘混合元方法有两个优越性:有限元空间不必满足L…  相似文献   

9.
基于计算机试验的均匀设计   总被引:5,自引:0,他引:5  
本文在计算机试验的基础上,提出了最小相关准则和最小距离离差准则,并将信息论中的Hamming距离和Lee距离引入到计算机试验中,证明了均匀设计在Hamming距离下的最优性和部分好格子点均匀设计在Lee距离下的最优性.基于偏差的考虑,给出了一类新的好格子点均匀设计和一个学习算法,利用这个学习算法,给出了基于Lee距离的最小距离离差准则的均匀设计表的构造方法.通过与已有的好格子点均匀设计和循环拉丁方均匀设计作比较,证明了文中的均匀设计在距离和偏差意义下有更好的均匀性.  相似文献   

10.
通过对最小度限制最小生成树(md-MST)问题性质进行分析,提出了一种基于边交换的贪心算法.算法先用贪心算法生成一棵生成树ST,然后对生成树ST经过边交换调整,得到满足问题约束条件的可行解,再对生成树ST进行进一步边交换优化,得到md-MST问题的最优解或接近最优解的近似解.实验证明,算法能在短对间内求出大规模顶点随机图的md-MST,是一种非常实用的求解md-MST问题的精确算法.  相似文献   

11.
This paper is concerned with the analysis of a control problem related to the optimal management of a bioreactor. This real-world problem is formulated as a state-control constrained optimal control problem. We analyze the state system (a complex system of partial differential equations modelling the eutrophication processes for non-smooth velocities), and we prove that the control problem admits, at least, a solution. Finally, we present a detailed derivation of a first order optimality condition - involving a suitable adjoint system - in order to characterize these optimal solutions, and some computational results.  相似文献   

12.
资产组合与缴费计划是待遇预定制养老基金管理的核心问题.针对此类养老基金的管理,建立Heston随机波动率模型,结合最优控制理论和Legendre变换,将原问题转化为对偶问题,通过对偶问题的求解,求得原问题的解析解,从而确定风险资产比例和缴费水平,最终实现养老基金管理的最优资产配置和最低缴费水平.  相似文献   

13.
Maximal hermitian solutions of the discrete algebraic matrix Riccati equation play an important role in least squares optimal control problems for discrete linear systems. We prove an existence and comparison theorem concerning maximal hermitian solutions. This theorem is inspired by known results for the algebraic Riccati equation arising in the least squares optimal control problem in continuous linear systems.  相似文献   

14.
We consider a nonlinear antiplane problem which models the deformation of an elastic cylindrical body in frictional contact with a rigid foundation. The contact is modelled with Tresca’s law of dry friction in which the friction bound is slip dependent.The aim of this article is to study an optimal control problem which consists of leading the stress tensor as close as possible to a given target, by acting with a control on the boundary of the body. The existence of at least one optimal control is proved. Next we introduce a regularized problem, depending on a small parameter ρ, and we study the convergence of the optimal controls when ρ tends to zero. An optimality condition is delivered for the regularized problem.  相似文献   

15.
We are concerned with the optimal control of time-fractional diffusion equations with missing boundary condition. Using the notion of no-regret control and least (or low) regret control developed by Lions, we first prove that the least regret control problem associated with the boundary fractional diffusion equation has a unique solution. Then we show that this solution converges to the no-regret control which we characterize by a singular optimality system.  相似文献   

16.
本文对具有状态终端约束、控制受限的非线性连续最优控制问题给出一种新的可实现的离散方法,此方法通过求解非线最小二乘问题避免这类问题离散后出现的不可行现象,文中给出这种做法的理论证明和实现方案。  相似文献   

17.
We consider a control problem in a Banach space with a bounded observer, but an unbounded controller which takes values in the extrapolated Favard class. A least square regulator problem can be formulated if the observer and the admissible controls take values in Hilbert spaces. We prove that for this type of LQR-problem the value function is given by a Riccati operator, and that a bounded state feedback based on the Riccati operator yields the optimal control. April 30, 1999  相似文献   

18.
In this work, we propose an approximate optimal control formulation of the Cauchy problem for the Stokes system. Here the problem is converted into an optimization one. In order to handle the instability of the solution of this ill-posed problem, a regularization technique is developed. We add a term in the least square function which happens to vanish while the algorithm converges. The efficiency of the proposed method is illustrated by numerical experiments.  相似文献   

19.
In Part 1 of the paper (Ref. 2), we have shown that the necessary conditions for the optimal control problem of the abort landing of a passenger aircraft in the presence of windshear result in a multipoint boundary-value problem. This boundary-value problem is especially well suited for numerical treatment by the multiple shooting method. Since this method is basically a Newton iteration, initial guesses of all variables are needed and assumptions about the switching structure have to be made. These are big obstacles, but both can be overcome by a so-called homotopy strategy where the problem is imbedded into a one-parameter family of subproblems in such a way that (at least) the first problem is simple to solve. The solution data to the first problem may serve as an initial guess for the next problem, thus resulting in a whole chain of problems. This process is to be continued until the objective problem is reached.Techniques are presented here on how to handle the various changes of the switching structure during the homotopy run. The windshear problem, of great interest for safety in aviation, also serves as an excellent benchmark problem: Nearly all features that can arise in optimal control appear when solving this problem. For example, the candidate for an optimal trajectory of the minimax optimal control problem shows subarcs with both bang-bang and singular control functions, boundary arcs and touch points of two state constraints, one being of first order and the other being of third order, etc. Therefore, the results of this paper may also serve as some sort of user's guide for the solution of complicated real-life optimal control problems by multiple shooting.The candidate found for an optimal trajectory is discussed and compared with an approximate solution already known (Refs. 3–4). Besides the known necessary conditions, additional sharp necessary conditions based on sign conditions of certain multipliers are also checked. This is not possible when using direct methods.An extended abstract of this paper was presented at the 8th IFAC Workshop on Control Applications of Nonlinear Programming and Optimization, Paris, France, 1989 (see Ref. 1).This paper is dedicated to Professor Hans J. Stetter on the occasion of his 60th birthday.  相似文献   

20.
In this paper, we consider a class of optimal control problem involving an impulsive systems in which some of its coefficients are subject to variation. We formulate this optimal control problem as a two-stage optimal control problem. We first formulate the optimal impulsive control problem with all its coefficients assigned to their nominal values. This becomes a standard optimal impulsive control problem and it can be solved by many existing optimal control computational techniques, such as the control parameterizations technique used in conjunction with the time scaling transform. The optimal control software package, MISER 3.3, is applicable. Then, we formulate the second optimal impulsive control problem, where the sensitivity of the variation of coefficients is minimized subject to an additional constraint indicating the allowable reduction in the optimal cost. The gradient formulae of the cost functional for the second optimal control problem are obtained. On this basis, a gradient-based computational method is established, and the optimal control software, MISER 3.3, can be applied. For illustration, two numerical examples are solved by using the proposed method.  相似文献   

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