共查询到20条相似文献,搜索用时 437 毫秒
1.
高毅 《高等学校计算数学学报》1998,20(3):201-208
1 引言 设为一闭凸锥,f是R~n到自身的一映射.广义互补问题,记作GCP(K,f),即找一向量x满足 GCP(K,f) x∈K,f(x)∈且x~Tf(x)=0,(1) 其中,是K的对偶锥(即对任一K中向量x,满足x~Ty≤0的所有y的集合).该问题首先 由Habetler和Price提出.当K=R_+~n(R~n空间的正卦限),此问题就是一般的互补问题.许多作者已经提出了很多求解线性或非线性互补问题的方法.例如:Dafermos,Fukushima,Harker和Price以及其它如参考文献所列.近年来,何针对单调线性变分不等式提出了一些投影收缩算法. Fang在函数是Lipschitz连续及强单调的条件下,在[3]给出一简单的迭代投影法,在[4]中给出一线性化方法去求解广义互补问题(1).在[3]中,他的迭代模式是 相似文献
2.
Anders Barrlund 《BIT Numerical Mathematics》1995,35(1):1-18
Three approaches for solving ODEs with invariants or DAEs are the constrained least squares method, the coordinate projection method and the derivative projection method. The stability properties of these three methods are compared for linear ODEs with linear invariants. There exist examples where each of the three approaches is to prefer. 相似文献
3.
《Optimization》2012,61(5):981-998
ABSTRACTIn this paper, we introduce several new extragradient-like approximation methods for solving variational inequalities in Hilbert spaces. Our algorithms are based on Tseng's extragradient method, subgradient extragradient method, inertial method, hybrid projection method and shrinking projection method. Strong convergence theorems are established under appropriate conditions. Our results extend and improve some related results in the literature. In addition, the efficiency of our algorithms is shown through numerical examples which are defined by the hybrid projection methods. 相似文献
4.
This paper presents a method for solving the linear semi-implicit
immersed boundary equations which avoids the severe time step restriction
presented by explicit-time methods. The Lagrangian variables are
eliminated via a Schur complement to form a purely Eulerian saddle
point system, which is preconditioned by a projection operator and
then solved by a Krylov subspace method. From the viewpoint of
projection methods, we derive an ideal preconditioner for the
saddle point problem and compare the efficiency of a number of simpler
preconditioners that approximate this perfect one.
For low Reynolds number and high stiffness,
one particular projection preconditioner
yields an efficiency improvement of the explicit IB method
by a factor around thirty.
Substantial speed-ups over explicit-time method are
achieved for Reynolds number below 100.
This speedup increases as the Eulerian grid size and/or the Reynolds number are further reduced. 相似文献
5.
针对属性权重已知而属性值为确数的多属性决策问题,提出了决策矩阵排序的投影法,并提出了关于投影法的三个定理及其证明.最后给出了两个相关例子说明本法的有效性和可行性. 相似文献
6.
7.
一族超线性收敛的投影拟牛顿算法 总被引:5,自引:0,他引:5
本文将梯度投影与拟牛顿法相结合,给出了求解一般线性约束非线性规划问题含两组参数的算法族.在一定的条件下证明了算法族的全局收敛性与它的子族的超线性收敛速度,并给出了投影D.F.P方法、投影BFGS方法等一些特例. 相似文献
8.
M. Yu. Pershagin 《Russian Mathematics (Iz VUZ)》2008,52(8):28-34
In this paper we propose a computational scheme of the general projection method for the solution of singular integrodifferential equations in the theory of stream lines and thermal conductivity. We theoretically substantiate this scheme from the standpoint of the theory of approximate methods of functional analysis. We consider particular cases of the general projection method, namely, the method of moments and the collocation method. 相似文献
9.
《Optimization》2012,61(10):1631-1648
ABSTRACTIn this paper, we develop a three-term conjugate gradient method involving spectral quotient, which always satisfies the famous Dai-Liao conjugacy condition and quasi-Newton secant equation, independently of any line search. This new three-term conjugate gradient method can be regarded as a variant of the memoryless Broyden-Fletcher-Goldfarb-Shanno quasi-Newton method with regard to spectral quotient. By combining this method with the projection technique proposed by Solodov and Svaiter in 1998, we establish a derivative-free three-term projection algorithm for dealing with large-scale nonlinear monotone system of equations. We prove the global convergence of the algorithm and obtain the R-linear convergence rate under some mild conditions. Numerical results show that our projection algorithm is effective and robust, and is more competitive with the TTDFP algorithm proposed Liu and Li [A three-term derivative-free projection method for nonlinear monotone system of equations. Calcolo. 2016;53:427–450]. 相似文献
10.
董云达 《高等学校计算数学学报》2010,32(3)
<正>This paper generalizes a class of projection type methods for monotone variational inequalities to general monotone inclusion.It is shown that when the normal cone operator in projection is replaced by any maximal monotone operator,the resulting method inherits all attractive convergence properties of projection type methods,and allows an adjusting step size rule.Weaker convergence assumption entails an extra projection at each iteration.Moreover,this paper also addresses applications of the resulting method to convex programs and monotone variational inequalities. 相似文献
11.
§1. IntroductionWeconsiderthefollowingoptimizationproblem:(P) minx∈Xf(x)(1)whereX={x|x∈En,gj(x)≤0,j=1,2,…,m;gj(x)=0,j=m+1,…,m+l},letI={1,2,…,m},L={m+1,…,m+l}.Fortheproblem(P)withL=,manyefficientprojectiontypealgorithms[1-11]havebeenproposed.In[12],… 相似文献
12.
用Levenberg-Marquardt类的投影收缩方法解运输问题 总被引:1,自引:0,他引:1
许碧欢 《高等学校计算数学学报》2004,26(3):203-213
For solving linear variational inequalities (LVI), the projection and contraction method of Levenberg-Marquardt type needs less iterations than an elementary projection and contraction method. However, the method of Levenberg-Marquardt type has to calculate the inverse of a matrix and hence it is unsuitable for large problems. In this paper, using the special structure of the constraint matrix, we present a PC method of Levenberg-Marquardt type for LVI arising from transportation problem without calculating any inverse matrices.Several computational experiments are presentded to indicate that the methods is good for solving the transportation problem. 相似文献
13.
For generalized eigenvalue problems, we consider computing all eigenvalues located in a certain region and their corresponding eigenvectors. Recently, contour integral spectral projection methods have been proposed for solving such problems. In this study, from the analysis of the relationship between the contour integral spectral projection and the Krylov subspace, we conclude that the Rayleigh–Ritz-type of the contour integral spectral projection method is mathematically equivalent to the Arnoldi method with the projected vectors obtained from the contour integration. By this Arnoldi-based interpretation, we then propose a block Arnoldi-type contour integral spectral projection method for solving the eigenvalue problem. 相似文献
14.
We study methods for solving a class of the quasivariational inequalities in Hilbert space when the changeable set is described by translation of a fixed, closed and convex set. We consider one variant of the gradient-type projection method and an extragradient method. The possibilities of the choice of parameters of the gradient projection method in this case are wider than in the general case of a changeable set. The extragradient method on each iteration makes one trial step along the gradient, and the value of the gradient at the obtained point is used at the first point as the iteration direction. In the paper, we establish sufficient conditions for the convergence of the proposed methods and derive a new estimate of the rates of the convergence. The main result of this paper is contained in the convergence analysis of the extragradient method. 相似文献
15.
In this paper, we proposed a simple and unconditional stable time-split Gauss–Seidel projection (GSP) method for the space fractional Landau–Lifshitz (FLL) equations. Numerical results are presented to demonstrate the effectiveness and stability of this method. 相似文献
16.
多指标决策与评价的新方法——主成份投影法 总被引:22,自引:0,他引:22
本文介绍了主成份投影法的原理和实施步骤 ,并对全国 31个省、自治区和直辖市的 1998年经济效益指标进行综合分析和排序 相似文献
17.
In recent papers Ruhe suggested a rational Krylov method for nonlinear eigenproblems knitting together a secant method for
linearizing the nonlinear problem and the Krylov method for the linearized problem. In this note we point out that the method
can be understood as an iterative projection method. Similarly to the Arnoldi method the search space is expanded by the direction
from residual inverse iteration. Numerical methods demonstrate that the rational Krylov method can be accelerated considerably
by replacing an inner iteration by an explicit solver of projected problems. 相似文献
18.
Dang Van Hieu Le Dung Muu Hoang Ngoc Duong Buu Huu Thai 《Mathematical Methods in the Applied Sciences》2020,43(17):9745-9765
In this paper, we introduce two new numerical methods for solving a variational inequality problem involving a monotone and Lipschitz continuous operator in a Hilbert space. We describe how to incorporate a regularization term depending on a parameter in the projection method and then establish the strong convergence of the resulting iterative regularization projection methods. Unlike known hybrid methods, the strong convergence of the new methods comes from the regularization technique. The first method is designed to work in the case where the Lipschitz constant of cost operator is known, whereas the second one is more easily implemented without this requirement. The reason is because the second method has used a simple computable stepsize rule. The variable stepsizes are generated by the second method at each iteration and based on the previous iterates. These stepsizes are found with only one cheap computation without line-search procedure. Several numerical experiments are implemented to show the computational effectiveness of the new methods over existing methods. 相似文献
19.
胡国雷 《高等学校计算数学学报》2001,23(4):378-384
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=… 相似文献
20.
CONSTRUCTIONS OF BASES FOR EXTENDED OBLIQUE PROJECTION METHOD 总被引:1,自引:0,他引:1
In this paper,we present some sufficient conditions for constructing the bases of the left and the right spaces to ensure the feasibility of the oblique projection method and the extended oblique projection method. 相似文献