A CONTINUATION HOMOTOPY METHOD FOR THE INVERSE PROBLEM OF OPERATOR IDENTIFICATION AND ITS APPLICATION

A new widly convergent method for solving the problem of operator kientification is illustrated.Numerical simulations are carried out to test the feasibllity and to study the general characteristics of the technique without the real measurement data.This technique is a direct application of the continuation homotopy method for solving nonlinear systems of equations.It is found that this method does give excellent results in solving the inverse problem of the elliptic differential equations.     

A hybrid method for inverse cavity scattering problem for shape

In this paper, we give a hybrid method to numerically solve the inverse open cavity scattering problem for cavity shape, given the scattered solution on the opening of the cavity. This method is a hybrid between an iterative method and an integral equations method for solving the Cauchy problem. The idea of this hybrid method is simple, the operation is easy, and the computation cost is small. Numerical experiments show the feasibility of this method, even for cases with noise.     

SOURCE TERM IDENTIFICATION WITH DISCONTINUOUS DUAL RECIPROCITY APPROXIMATION AND QUASI-NEWTON METHOD FROM BOUNDARY OBSERVATIONS

This paper deals with discontinuous dual reciprocity boundary element method for solving an inverse source problem.The aim of this work is to determine the source term in elliptic equations for nonhomogenous anisotropic media,where some additional boundary measurements are required.An equivalent formulation to the primary inverse problem is established based on the minimization of a functional cost,where a regularization term is employed to eliminate the oscillations of the noisy data.Moreover,an efficient algorithm is presented and tested for some numerical examples.     

反中心对称矩阵的广义特征值反问题

Given matrix X and diagonal matrix A , the anti-centrosymmetric solutions (A, B) and its optimal approximation of inverse generalized eigenvalue problem AX = BXA have been considered. The general form of such solutions is given and the expression of the optimal approximation solution to a given matrix is derived. The algorithm and one numerical example for solving optimal approximation solution are included.     

Successive projection method for solving the unbalanced Procrustes problem

We present a successive projection method for solving the unbalanced Procrustes problem: given matrix A∈Rn×n and B∈Rn×k, n>k, minimize the residual‖AQ-B‖F with the orthonormal constraint QTQ = Ik on the variant Q∈Rn×k. The presented algorithm consists of solving k least squares problems with quadratic constraints and an expanded balance problem at each sweep. We give a detailed convergence analysis. Numerical experiments reported in this paper show that our new algorithm is superior to other existing methods.     

A RELAXED INERTIAL FACTOR OF THE MODIFIED SUBGRADIENT EXTRAGRADIENT METHOD FOR SOLVING PSEUDO MONOTONE VARIATIONAL INEQUALITIES IN HILBERT SPACES

In this paper,we investigate pseudomonotone and Lipschitz continuous variational inequalities in real Hilbert spaces.For solving this problem,we propose a new method that combines the advantages of the subgradient extragradient method and the projection contraction method.Some very recent papers have considered different inertial algorithms which allowed the inertial factor is chosen in [0;1].The purpose of this work is to continue working in this direction,we propose another inertial subgradien...     

Least-Squares Solution of Inverse Problem for Hermitian Anti-reflexive Matrices and Its Appoximation

In this paper, we first consider the least-squares solution of the matrix inverse problem as follows： Find a hermitian anti-reflexive matrix corresponding to a given generalized reflection matrix J such that for given matrices X, B we have minA ｜｜AX - B｜｜. The existence theorems are obtained, and a general representation of such a matrix is presented. We denote the set of such matrices by SE. Then the matrix nearness problem for the matrix inverse problem is discussed. That is： Given an arbitrary A^＊, find a matrix A E SE which is nearest to A^＊ in Frobenius norm. We show that the nearest matrix is unique and provide an expression for this nearest matrix.     

The Inverse Problem of Centrosymmetric Matrices with a Submatrix Constraint

By using Moore-Penrose generalized inverse and the general singular value decomposition of matrices, this paper establishes the necessary and sufficient conditions for the existence of and the expressions for the centrosymmetric solutions with a submatrix constraint of matrix inverse problem AX = B. In addition, in the solution set of corresponding problem, the expression of the optimal approximation solution to a given matrix is derived.     

MULTI-SCALE METHODS FOR INVERSE MODELING IN 1-D MOS CAPACITOR

In this paper,we investigate multi-scale methods for the inverse modeling in 1-D Metal-Oxide-Silicon(MOS) capactior,First,the mathematical model of the device is given and the numerical simulation for the forward problem of the model is implemented using finite element method with adaptive moving mesh. Then numerical analysis of these parameters in the model for the inverse problems is presented .Some matrix analysis tools are applied to explore the parameters‘ sensitivities,And thired,the parameters are extracted using Levenberg-Marquardt optimization method.The essential difficulty arises from the effect of multi-scale physical differeence of the parameters.We explore the relationship between the parameters‘ sensitivitites and the sequencs for optimization,which can seriously affect the final inverse modeling results.An optimal sequence can efficiently overcome the multip-scale problem of these parameters,Numerical experiments show the efficiency of the proposed methods.     

A NEW SELF-ADAPTIVE ITERATIVE METHOD FOR GENERAL MIXED QUASI VARIATIONAL INEQUALITIES

The general mixed quasi variational inequality containing a nonlinear term φ is a useful and an important generalization of variational inequalities. The projection method can not be applied to solve this problem due to the presence of nonlinear term. It is well known that the variational inequalities involving the nonlinear term φ are equivalent to the fixed point problems and resolvent equations. In this article, the authors use these alternative equivalent formulations to suggest and analyze a new self-adaptive iterative method for solving general mixed quasi variational inequalities. Global convergence of the new method is proved. An example is given to illustrate the efficiency of the proposed method.     

Solving a class of matrix minimization problems by linear variational inequality approaches

A class of matrix optimization problems can be formulated as a linear variational inequalities with special structures. For solving such problems, the projection and contraction method (PC method) is extended to variational inequalities with matrix variables. Then the main costly computational load in PC method is to make a projection onto the semi-definite cone. Exploiting the special structures of the relevant variational inequalities, the Levenberg-Marquardt type projection and contraction method is advantageous. Preliminary numerical tests up to 1000×1000 matrices indicate that the suggested approach is promising.     

一种基于LVI求解二次规划问题的数值算法

给出并研究了一种数值算法(简称94LVI算法),用于求解带等式和双端约束的二次规划问题. 这类带约束的二次规划问题首先被转换为线性变分不等式问题,该问题等价于分段线性投影等式.接着使用94LVI算法求解上述分段线性投影等式,从而得到QP问题的最优解. 进一步给出了94LVI算法的全局收敛性证明. 94LVI算法与经典有效集算法的对比实验结果证实了给出的94LVI算法在求解二次规划问题上的高效性与优越性.     

A self-adaptive projection and contraction algorithm for the traffic assignment problem with path-specific costs

This paper considers solving a special case of the nonadditive traffic equilibrium problem presented by Gabriel and Bernstein [Transportation Science 31 (4) (1997) 337–348] in which the cost incurred on each path is made up of the sum of the arc travel times plus a path-specific cost for traveling on that path. A self-adaptive projection and contraction method is suggested to solve the path-specific cost traffic equilibrium problem, which is formulated as a nonlinear complementarity problem (NCP). The computational effort required per iteration is very modest. It consists of only two function evaluations and a simple projection on the nonnegative orthant. A self-adaptive technique is embedded in the projection and contraction method to find suitable scaling factor without the need to do a line search. The method is simple and has the ability to handle a general monotone mapping F. Numerical results are provided to demonstrate the features of the projection and contraction method.     

Inverse Problems for Identification of Memory Kernels in Viscoelasticity

Inverse problems for identification of the memory kernel in the linear constitutive stress–strain relation of Boltzmann type are reduced to a non-linear Volterra integral equation using Fourier's method for solving the direct problem. To this equation the contraction principle in weighted norms is applied. In this way global existence of a solution to the inverse problem is proved and stability estimates for it are derived. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.     

求解大规模带二次简单约束的二次规划的显式自调比投影收缩算法

1　引　　言我们来考虑如下的带二次简单约束的二次规划问题12 x TH x +c Tx =mins.t.,‖ x‖ 2 ≤ a (1)其中 H∈ Rn× n是一个半正定对称矩阵 ,c∈ Rn,这里 a是一个确定的参数 .求解问题 (1)的最基本的方法是构造 L agrange函数 :L (x,λ) =x TH x +2 c Tx +λ(x Tx - a2 ) (2 )当约束起作用时 ,由 x L (x,λ) =0 ,　　 λL (x,λ) =0 ,得H x +c+λx =0‖ x‖ =a (3)即(H +λI) x +c =0‖ x‖ =a从而有‖ (H +λI) - 1 c‖ =a令φ(λ) =‖ (H +λI) - 1 c‖ ,　　 S(λ) =(H +λI) - 1 c则φ2 (λ) =STS =c T(H +λI) - 2 c=…     

交替方向法求解带线性约束的变分不等式

１引言变分不等式是一个有广泛应用的数学问题,它的一般形式是：确定一个向量,使其满足这里ｆ是一个从到自身的一个映射,Ｓ是Ｒ中的一个闭凸集．在许多实际问题中集合Ｓ往往具有如下结构其中ＡｂＫ是中的一个简单闭凸集．例如一个正卦限,一个框形约束结构,或者一个球简言之,Ｓ是Ｒ中的一个超平面与一个简单闭凸集的交．求解问题（１）－（２）,往往是通过对线性约束Ａ引人Ｌａｇｒａｎｇｅ乘子,将原问题化为如下的变分不等式：确定使得我们记问题（３）－（４）为ＶＩ（Ｆ）．熟知［３］,ＶＩ（,Ｆ）等价于投影方程其中凡（·）表…     

Convergence Properties of Projection and Contraction Methods for Variational Inequality Problems

In this paper we develop the convergence theory of a general class of projection and contraction algorithms (PC method), where an extended stepsize rule is used, for solving variational inequality (VI) problems. It is shown that, by defining a scaled projection residue, the PC method forces the sequence of the residues to zero. It is also shown that, by defining a projected function, the PC method forces the sequence of projected functions to zero. A consequence of this result is that if the PC method converges to a nondegenerate solution of the VI problem, then after a finite number of iterations, the optimal face is identified. Finally, we study local convergence behavior of the extragradient algorithm for solving the KKT system of the inequality constrained VI problem. \keywords{Variational inequality, Projection and contraction method, Predictor-corrector stepsize, Convergence property.} \amsclass{90C30, 90C33, 65K05.} Accepted 5 September 2000. Online publication 16 January 2001.     

对称的运输问题及其逆问题

本文对［１,２,６］中提出的运输问题进行了推广,并提出了一个强多项式算法,从而改进了原有的结果．同时对对称的运输问题的逆问题进行了研究,并借助于最小费用循环流技术得到了一个强多项式算法．     

Solution of projection problems over polytopes

Summary In this paper, we present variants of a convergent projection and contraction algorithm [25] for solving projection problems over polytope. By using the special struture of the projection problems, an iterative algorithm with constant step-size is given, which is globally linearly convergent. These algorithms are simple to implement and each step of the method requires only a few matrix-vector multiplications. Especially, for minimums norm problems over transportation or general network polytopes onlyO(n) additions andO(n) multiplications are needed at each iteration. Numerical results for randomly generated test problems over network polytopes, up to 10000 variables, indicate that the presented algorithms are simple and efficient even for large problems.     

ON THE SEPARABLE NONLINEAR LEAST SQUARES PROBLEMS

Separable nonlinear least squares problems are a special class of nonlinear least squares problems, where the objective functions are linear and nonlinear on different parts of variables. Such problems have broad applications in practice. Most existing algorithms for this kind of problems are derived from the variable projection method proposed by Golub and Pereyra, which utilizes the separability under a separate framework. However, the methods based on variable projection strategy would be invalid if there exist some constraints to the variables, as the real problems always do, even if the constraint is simply the ball constraint. We present a new algorithm which is based on a special approximation to the Hessian by noticing the fact that certain terms of the Hessian can be derived from the gradient. Our method maintains all the advantages of variable projection based methods, and moreover it can be combined with trust region methods easily and can be applied to general constrained separable nonlinear problems. Convergence analysis of our method is presented and numerical results are also reported.