一种求约束总极值的水平值估计方法

给出了一种求约束总极值的水平值估计方法,说明了修正的方差方程的根与原始问题的最优值之间的等价性,给出了一种基于牛顿法的水平值估计算法并证明了实现算法的收敛性．初步的计算例子表明所给算法是有效的．     

一种新的求总极值的水平值估计算法

提出了一种求解总极值问题的新水平值估计算法. 为此, 引入一类变差函数并研究它的性质; 给出基于变差函数的全局最优性条件, 并构造出一种求总极值的水平值估计算法. 为了实现这种算法, 采用了基于重点样本技术的Monte-Carlo方法来计算变差,并利用相对熵算法的主要思想更新取样密度.初步的数值实验说明了算法的有效性.     

二阶退化双曲型方程的Darboux型问题

本文讨论二阶退化双曲型方程的一些边值问题.文中先给出第一Darboux问题和一般斜微商边值问题的提法和解的表示式,然后使用复分析方法证明了上述问题解的存在唯一性.     

一种修正的求总极值的积分—水平集方法的实现算法收敛性

1978年,郑权等提出了一个积分型求总极值的概念性算法及Monte-Carlo随机投点的实现算法,给出了概念性算法的总极值存在的充分必要条件,但是其实现算法收敛性仍未解决,1986年,张连生等给出离散均值－水平集的实现算法,并证明了它的收敛性。本文给出修正的积分－水平集方法,用一致分布搂九值积分逼近水平集构造实现算法,并证明了算法的收敛性。     

具C^∞系数的非主型方程的Goursat问题

本文以逼近和正则化方法，对一类具Ｃ＾∞系数和数据的非主型方程的Ｇｏｕｒｓａｔ问题证明了Ｃ＾∞解的存在唯一性。     

离散型随机变量数学期望的几种巧妙算法

利用定义求解离散型随机变量的数学期望有时显得非常复杂,本文给出了三种巧妙计算离散型随机变量数学期望的方法:对称性法、随机变量分解法、公式演变法.计算过程非常简洁,达到了简化计算的目的.     

有限维逼近无限维总极值的水平值估计方法

变分计算、最优控制、微分对策等常常要求考虑无限维空间中的总极值问题,但实际计算中只能得出有限维空间中的解.本文用有限维逼近无限维的方法来讨论函数空间中的总体最优化问题.用水平值估计和变侧度方法来求得有限维逼近总体最优化问题.对于有约束问题,用不连续精确罚函数法将其转化为无约束问题求解.     

一类高阶非线性双曲型方程Cauchy问题解的爆破

本文研究一类高阶非线性双曲型方程utt-uxx+μuxxx-αuxxtt+βuxxxxtt=f(ux)x的Cauchy问题,证明问题解的存在性与唯一性,并给出解在有限时刻爆破的充分条件.     

数学期望型水平值逼近全局最小值的方法

郑权在1978年提出的一种积分水平集算法概念性算法.由于水平集一般情况下难以求出,此算法通过Monte-Carlo随机取点来实现.本文提出了数学期望型水平值逼近全局最小值的概念性算法,它利用了相对熵主要思想,通过改变重要样本密度函数,克服了郑权算法水平集不易求得而难以求出水平值的困难.本文还给出了求全局最小值的收敛准则并证明了它的渐进收敛性.     

集值非线性混合变分包含问题的一类新的迭代算法

在Hilbert空间中讨论一类广义集值非线性混合变分包含问题近似解的存在性，建立变分包含与广义预解方程的等价性，形成了迭代算法并研究了算法的收敛性．     

一类单调函数的数学期望

对一类单调可微的有界函数 ,利用相对变化率的概念 ,定义了一种由该函数生成的概率密度函数 ,讨论了有关数学期望的计算和性质 ,并给出了在函数上升或下降速度比较、药动学模型识别中的应用 .     

Approximation Properties of a Special Class of Mathematical Expectation Operators

61-IntroductionLet(X.}"cNbeasequenceofindependentrandomvariableseachhavingthesamelatticepointdistributionwithprobabilityfunctionP(X,=a kh)=P*,expectationEX"=),l(x)andvarianceE(X"-ax")'=a2(x).WhereKeZ:={o,tl,l2,..'},a,harethepositivecon-stants,xeI=Y'=Ri8arealcontinuousparameter.LettheprobabilitydistributionofS,=ZX,beForacontinuousfunctionfontheinterval7'(possiblyinfinite)definethemathematicalex-pectationoperatorRemarks(l)UsingChebychev,sinequalitywegeteasily.(See[1,P,,,f,,.j)-(2)Manyo…     

On a Minimum Linear Classification Problem

We study the following linear classification problem in signal processing: Given a set Bof n black point and a set W of m white points in the plane (m = O(n)), compute a minimum number of lines L such that in the arrangement of L each face contain points with the same color (i.e., either all black points or all white points). We call this the Minimum Linear Classification (MLC) problem. We prove that MLC is NP-complete by a reduction from the Minimum Line Fitting (MLF) problem; moreover, a C-approximation to MLC implies a C-approximation to the MLF problem. Nevertheless, we obtain an O(log n)-factor algorithm for MLC and we also obtain an O(log Z)-factor algorithm for MLC where Z is the minimum number of disjoint axis-parallel black/white rectangles covering B and W.     

On a Minimum Linear Classification Problem

We study the following linear classification problem in signal processing: Given a set B of n black point and a set W of m white points in the plane (m=O(n)), compute a minimum number of lines L such that in the arrangement of L each face contain points with the same color (i.e., either all black points or all white points). We call this the Minimum Linear Classification (MLC) problem. We prove that MLC is NP-complete by a reduction from the Minimum Line Fitting (MLF) problem; moreover, a C-approximation to Minimum Linear Classification implies a C-approximation to the Minimum Line Fitting problem. Nevertheless, we obtain an O(log _n )-factor algorithm for MLC and we also obtain an O(log _Z)-factor algorithm for MLC where Z is the minimum number of disjoint axis-parallel black/white rectangles covering B and W.     

On a Global Optimization Problem in the Study of Information Discrepancy

A nonlinear function has been introduced for indexing the disagreementdegree of a group of judgment matrices (Weiwu Fang, 1994). It has many goodproperties and may be applied in decision making and information processes.In this paper, we will discuss a global optimization problem concerned withthe global maximum of this function which is constrained on some sets ofmatrices. Because the size of matrix groups in the problem is arbitrary andthe number of local maximum solutions increases exponentially, numericalmethods are not suitable and formalized results are desired for the problem.By an approach somewhat similar to the branch and bound method, we haveobtained some formulae on global maximums, a sufficient and necessarycondition of the function taking the maximums, and some maximum solutionsets.     

一种无约束全局优化的水平值下降算法

本文研究无约束全局优化问题,建立了一种新的水平值下降算法(Level-value Descent Method,LDM).讨论并建立了概率意义下取全局最小值的一个充分必要条件,证明了算法LDM是依概率测度收敛的.这种LDM算法是基于重点度取样(Improtance Sampling)和Markov链Monte-Carlo随机模拟实现的,并利用相对熵方法(TheCross-Entropy Method)自动更新取样密度,算例表明LDM算法具有较高的数值精度和较好的全局收敛性.     

一类脉冲控制模型的最小费用问题

本文研究了一类脉冲控制模型的最小费用问题,在一定条件下,给出了相应的最佳费用函数具体解析式．     

一类奇异边值问题解的存在性

在非线性项系数无界的情形下，得到了一类半线性椭圆型方程爆破解的存在性。     

A Class of Global Optimization Problems as Models of the Phase Unwrapping Problem

Let I={(i,j) i=1, 2,..., N ₁, j=1, 2,..., N ₂} and let U=U_i,j, (i,j)I be a discrete real function defined on I. Let []₂ be modulus 2, we define W:I , ) as follows W=[U]₂. The function U will be called phase function and the function W will be called wrapped phase function. The phase unwrapping problem consists in recovering U from some knowledge of W. This problem is not well defined, that is infinitely many functions U correspond to the same function W, and must be `regularized' to be satisfactorily solvable. We propose several formulations of the phase unwrapping problem as an integer nonlinear minimum cost flow problem on a network. Numerical algorithms to solve the minimum cost flow problems obtained are proposed. The phase unwrapping problem is the key problem in interferometry, we restrict our attention to the SAR (Synthetic Aperture Radar) interferometry problem. We compare the different formulations of the phase unwrapping problem proposed starting from the analysis of the numerical experience obtained with the numerical algorithms proposed on synthetic and real SAR interferometry data. The real data are taken from the ERS missions of the European Space Agency (ESA).