基于服装舒适性的纺织材料设计反问题

纺织材料设计反问题是数学物理反问题的一个新领域,也被称为应用数学与计算数学的一个分支.综述纺织材料设计反问题的来源、数学归结,并基于服装的热湿舒适性、压力舒适性提出了设计反问题,给出了反问题解的定义,综述了求解纺织材料设计反问题的数值算法,列举了若干具有挑战的研究课题.     

有奇异解的无约束最优化问题的一种混合法

本文研究求解含有奇异解的无约束最优化问题算法 .该类问题的一个重要特性是目标函数的Hessian阵可能处处奇异 .我们提出求解该类问题的一种梯度 -正则化牛顿型混合算法 .并在一定的条件下得到了算法的全局收敛性 .而且 ,经一定迭代步后 ,算法还原为正则化 Newton法 .因而 ,算法具有局部二次收敛性 .     

一类逆时反问题的改进正则化方法的收敛性

1引 言 非线性反问题广泛地存在于许多科学和工程问题中,反问题求解的主要困难在于问题的不适定性,即待求函数或参量不连续依赖于观测数据.用来求解非线性不适定问题的方法主要有Tikhonov正则化方法和迭代正则化方法[1,2,3,4].Tikhonov正则化方法是通过引入正则化参数及稳定泛函,将目标泛函离散化,从而得到解的一个稳定近似,即正则化解.     

一种统一的非凸稀疏恢复的原始对偶有效集算法

研究了基于最小二乘法的稀疏信号恢复问题.针对一类非凸稀疏性罚,包括l^0、bridge、capped-l^1、光滑剪切绝对差和极小极大凹罚,提出了一种新的原始对偶有效集算法.首先证明相关优化问题的全局极小值的存在性,然后利用相关阈值算子,推导出全局极小值的一个新的必要最优条件,必要最优条件的解是坐标极小值,在一定条件下,它们也是局部的极小值.引入对偶变量后,可同时使用原变量和对偶变量确定有效集.此外,这种关系适用于一种有效集类迭代算法,该算法在每一步中首先只更新有效集上的原始变量,然后显式地更新对偶变量.结合正则化参数的延拓性,证明了原始对偶有效集方法在一定正则化条件下全局收敛于潜在回归目标.大量的数值实验表明,与现有的稀疏恢复方法相比,该方法具有较高的效率和精度.     

求解病态线性方程组的误差转移法和增广方程组法的机理及算法改进

为获得病态线性方程组的高精度解,建立了一种优化模型,其最优解等价于早先提出的误差转移法和增广方程组法;指出后两者的本质机理是通过极小化解的模来近似极小化解的误差.为使算法适用于数据有污染的情况,进行了正则化改造.证明了新算法理论上与Tikhonov正则化等价.但当正则化参数趋于0时,目标函数的不同使得两者性能迥异,新算法可直接用于数据无污染的情况,而后者仍需选取合适的正则参数.数值算例验证了算法的有效性.     

一个分数阶生长-抑制系统的参数反问题

本文研究一个分数阶生长-抑制线性系统模型及其参数反问题.首先利用Laplace逆变换得到正问题解的唯一存在性.其次,考虑一个利用内点观测数据确定微分阶数与衰减率的反问题,应用极值原理在Laplace像空间中证明反演的唯一性.最后,基于正问题的有限差分解,应用同伦正则化算法进行数值反演.计算结果表明算法的收敛性及反问题的数值稳定性.     

双调和方程柯西问题的修正的Tikhonov正则化方法

本文研究了双调和方程柯西问题,这类是不适定的,即问题的解(如果存在)不连续依赖于测量数据.首先在精确解的先验假设下给出问题的条件稳定性结果.接着利用修正的Tikhonov正则化方法求解此不适定问题.在先验和后验正则化参数选取规则下,给出正则解和精确解之间的误差估计式.最后给出几个数值例子验证此正则化方法求解此类反问题的有效性.     

求解一维侧边热传导方程反问题的正则化方法

研究了一维侧边热传导方程反问题.在求解一维侧边热传导方程的基础上,利用数值积分法进行离散化处理,然后引入正则化方法,采用偏差原理确定正则化参数,从而得到一维侧边热传导方程反问题的数值解.数值模拟结果表明,给出的正则化方法对于求解一维侧边热传导方程反问题是可行有效的.     

非线性不适定问题的正则化方法

本文考虑非线性不适定问题Tx=y的近似求解,利用Тихоноь正则化方法来逼近问题的x-极小模解,当算子和右端都近似已知时,给出一种决定正则化参数的方法,并给出正则解的收效性和渐近收敛阶估计。     

一类偏积分-微分方程中的反问题

对一类偏积分-微分方程中参数校准的反问题进行研究.在弱解的框架下,原问题可转化为含具体正则化项的最优化问题.文中证明了该最优化问题的解的存在性和稳定性,并考察了最优解存在的一阶必要条件.另外,证明了当正则化参数足够大时,该最优化问题关于参数a的凸性性质.基于偏积分-微分方程反问题的研究对于金融市场中的模型校准问题具有重要的意义.     

Textile porosity determination based on a nonlinear heat and moisture transfer model

The inverse problems of textile materials design on heat and moisture transfer properties are important and indispensable in applications in the body-clothing-environment system. We present an inverse problem of textile porosity determination (IPTPD) based on a nonlinear heat and moisture transfer model. Adopting the idea of the least-squares, the mathematical formulation of IPTPD is deduced to a regularized optimization problem with collocation method applied. The continuity of the regularized minimization problem is proved. By means of genetic algorithm (GA), the approximate solution of the IPTPD is numerically obtained. To reduce the computational cost, an improved algorithm based on BP neural network with GA is proposed in the numerical simulation. Compared with the direct GA searching, the computational cost is greatly reduced, which presents a similar result.     

The inverse problem for the simplified system of equations of heat-moisture transport

In solving an auxiliary Cauchy problem for the simplified system of equations for heat-moisture transport we find new inversion formulas of the symbolic Fantappiè method whose use makes it possible to determine two coefficients in explicit form in boundary conditions of third kind for the problem without initial conditions for fixed t for the same system of equations of heat-moisture transport.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 34, 1991, pp. 47–50.     

Generalized reflected BSDEs driven by a Lévy process and an obstacle problem for PDIEs with a nonlinear Neumann boundary condition

In this paper, we derive the existence and uniqueness of the solution for a class of generalized reflected backward stochastic differential equations (GRBSDEs in short) driven by a Lévy process, which involve the integral with respect to a continuous process by means of the Snell envelope, the penalization method and the fixed point theorem. In addition, we obtain the comparison theorem for the solutions of the GRBSDEs. As an application, we give a probabilistic formula for the viscosity solution of an obstacle problem for a class of partial differential-integral equations (PDIEs in short) with a nonlinear Neumann boundary condition.     

An inverse problem of Bilayer textile thickness determination in dynamic heat and moisture transfer

An inverse problem of bilayer textile thickness determination in dynamic heat and moisture transfer is presented satisfying the heat–moisture comfort level of human body. Heat and mass transfer law in bilayer textiles is displayed by proving the existence and uniqueness of solution to the coupled partial differential equations with initial-boundary value conditions. The finite difference method is employed to derive the numerical solution to partial differential equations. The regularized solution of the inverse problem is reformulated into solving function minimum problem through the Tikhonov regularization method. The golden section method is applied to solve the direct search problem and achieve the optimal solution to the inverse problem. Numerical algorithm and its numerical results provide theoretical explanation for textile materials research and development.     

基于正弦型光滑打磨函数对0-1规划问题的连续化求解方法

传统的求解0-1规划问题方法大多属于直接离散的解法.现提出一个包含严格转换和近似逼近三个步骤的连续化解法:(1)借助阶跃函数把0-1离散变量转化为[0,1]区间上的连续变量;(2)对目标函数采用逼近折中阶跃函数近光滑打磨函数,约束条件采用线性打磨函数逼近折中阶跃函数,把0-1规划问题由离散问题转化为连续优化模型;(3)利用高阶光滑的解法求解优化模型.该方法打破了特定求解方法仅适用于特定类型0-1规划问题惯例,使求解0-1规划问题的方法更加一般化.在具体求解时,采用正弦型光滑打磨函数来逼近折中阶跃函数,计算效果很好.     

Perturbation analysis of the heat transfer in porous media with small thermal conductivity

An approximate analytical solution for the one-dimensional problem of heat transfer between an inert gas and a porous semi-infinite medium is presented. Perturbation methods based on Laplace transforms have been applied using the solid thermal conductivity as small parameter. The leading order approximation is the solution of Nusselt (or Schumann) problem. Such solution is corrected by means of an outer approximation. The boundary condition at the origin has been taking into account using an inner approximation for a boundary layer. The gas temperature presents a discontinuous front (due to the incompatibility between initial and boundary conditions) which propagates at constant velocity. The solid temperature at the front has been smoothed out using an internal layer asymptotic approximation. The good accuracy of the resulting asymptotic expansion shows its usefulness in several engineering problems such as heat transfer in porous media, in exhausted chemical reactions, mass transfer in packed beds, or in the analysis of capillary electrochromatography techniques.     

Series solution for heat transfer from a continuous surface in a parallel free stream of viscoelastic fluid

This work is concerned with the influence of uniform suction or injection on flow and heat transfer analysis of a second order fluid. The resulting nonlinear problem for velocity is solved by means of homotopy analysis method (HAM). The comparison between the numerical solution of Hady and Gorla (Acta Mec 128 (1998), 201–208 and HAM solution is discussed with the help of numerical tables and graphs. Nonsimilar solutions to the stream function and temperature are developed. The influence of important parameters is seen on the velocity, temperature, skin friction coefficient, and temperature gradient. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 27: 1511–1524, 2011     

A new analytical solution branch for the Blasius equation with a shrinking sheet

A similarity equation of the momentum boundary layer is analytically studied for a moving flat plate with mass transfer in a stationary fluid by a newly developed technique namely homotopy analysis method (HAM). The equation shows its significance for the practical problem of a shrinking sheet with a constant velocity, and only admits the existence of the solution with mass suction at the wall surface. The present work provides analytically new solution branch of the Blasius equation with a shrinking sheet in different solution areas, including both multiple solutions and unique solution with the aid of an introduced auxiliary function. The analytical results show that quite complicated behavior with three different solution areas controlled by two critical mass transfer parameters exists, which agrees well with the numerical techniques and greatly differs from the continuously stretching surface problem and the Blasius problem with a free stream. The new analytical solution branch of the Blasius equation with a shrinking sheet enriches the solution family of the Blasius equation, and helps to deeply understand the Blasius equation.     

Euler Discretization and Inexact Restoration for Optimal Control

A computational technique for unconstrained optimal control problems is presented. First, an Euler discretization is carried out to obtain a finite-dimensional approximation of the continuous-time (infinite-dimensional) problem. Then, an inexact restoration (IR) method due to Birgin and Martínez is applied to the discretized problem to find an approximate solution. Convergence of the technique to a solution of the continuous-time problem is facilitated by the convergence of the IR method and the convergence of the discrete (approximate) solution as finer subdivisions are taken. The technique is numerically demonstrated by means of a problem involving the van der Pol system; comprehensive comparisons are made with the Newton and projected Newton methods.