共查询到20条相似文献,搜索用时 171 毫秒
1.
Min Li 《Numerical Functional Analysis & Optimization》2013,34(3):310-322
An algorithm for solving nonlinear monotone equations is proposed, which combines a modified Liu-Storey conjugate gradient method with hyperplane projection method. Under mild conditions, the global convergence of the proposed method is established with a suitable line search method. The method can be applied to solve large-scale problems for its lower storage requirement. Numerical results indicate that our method is efficient. 相似文献
2.
Since 1965, there has been significant progress in the theoretical study on quasi-Newton methods for solving nonlinear equations, especially in the local convergence analysis. However, the study on global convergence of quasi-Newton methods is relatively fewer, especially for the BFGS method. To ensure global convergence, some merit function such as the squared norm merit function is typically used. In this paper, we propose an algorithm for solving nonlinear monotone equations, which combines the BFGS method and the hyperplane projection method. We also prove that the proposed BFGS method converges globally if the equation is monotone and Lipschitz continuous without differentiability requirement on the equation, which makes it possible to solve some nonsmooth equations. An attractive property of the proposed method is that its global convergence is independent of any merit function.We also report some numerical results to show efficiency of the proposed method.
3.
本文在著名PRP共轭梯度算法的基础上研究了一种无导数谱PRP投影算法,并证明了算法在求解带有凸约束条件的非线性单调方程组问题的全局收敛性.由于无导数和储存量小的特性,它更适应于求解大规模非光滑的非线性单调方程组问题.数值试验表明,新算法对给定的测试问题是有效的和稳定的. 相似文献
4.
陈香萍 《数学的实践与认识》2017,(13):168-175
推广了一种修正的CG_DESCENT共轭梯度方法,并建立了一种有效求解非线性单调方程组问题的无导数投影算法.在适当的线搜索条件下,证明了算法的全局收敛性.由于新算法不需要借助任何导数信息,故它适应于求解大规模非光滑的非线性单调方程组问题.大量的数值试验表明,新算法对给定的测试问题是有效的. 相似文献
5.
借助谱梯度法和HS共轭梯度法的结构, 建立一种求解非线性单调方程组问题的谱HS投影算法. 该算法继承了谱梯度法和共轭梯度法储存量小和计算简单的特征,
且不需要任何导数信息, 因此它适应于求解大规模非光滑的非线性单调方程组问题. 在适当的条件下, 证明了该算法的收敛性, 并通过数值实验表明了该算法的有效性. 相似文献
6.
We introduce a regularized Newton method coupled with the parallel splitting-up technique for solving nonlinear ill-posed
equations with smooth monotone operators. We analyze the convergence of the proposed method and carry out numerical experiments
for nonlinear integral equations. 相似文献
7.
8.
N. Ya. Moiseev 《Computational Mathematics and Mathematical Physics》2011,51(4):676-687
An approach to the construction of high-order accurate monotone difference schemes for solving gasdynamic problems by Godunov’s
method with antidiffusion is proposed. Godunov’s theorem on monotone schemes is used to construct a new antidiffusion flux
limiter in high-order accurate difference schemes as applied to linear advection equations with constant coefficients. The
efficiency of the approach is demonstrated by solving linear advection equations with constant coefficients and one-dimensional
gasdynamic equations. 相似文献
9.
Igor Boglaev 《Numerical Methods for Partial Differential Equations》2012,28(2):621-640
This article deals with numerical solutions of a general class of coupled nonlinear elliptic equations. Using the method of upper and lower solutions, monotone sequences are constructed for difference schemes which approximate coupled systems of nonlinear elliptic equations. This monotone convergence leads to existence‐uniqueness theorems for solutions to problems with reaction functions of quasi‐monotone nondecreasing, quasi‐monotone nonincreasing and mixed quasi‐monotone types. A monotone domain decomposition algorithm which combines the monotone approach and an iterative domain decomposition method based on the Schwarz alternating, is proposed. An application to a reaction‐diffusion model in chemical engineering is given. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 28: 621–640, 2012 相似文献
10.
提出一种求解强单调非线性方程组的BFGS算法,该算法的一个明显优点是Bκ的条件数比Li-Fukushima^[3]提出的GNBFGS中Bκ的条件数小得多。且该算法是一种无需计算导数的下降算法。在一定的条件下,证明了算法的全局收敛性和超线性收敛性。最后进行数值试验,结果表明,本文算法具有较好的数值结果。而且验证了本文所提出的算法中Bκ的条件数要比GNBFGS算法的条件数小得多。 相似文献
11.
An iterative scheme for solving ill-posed nonlinear operator equations with monotone operators is introduced and studied in
this paper. A discrete version of the Dynamical Systems Method (DSM) algorithm for stable solution of ill-posed operator equations
with monotone operators is proposed and its convergence is proved. A discrepancy principle is proposed and justified. A priori and a posteriori stopping rules for the iterative scheme are formulated and justified.
AMS subject classification (2000) 47J05, 47J06, 47J35, 65R30 相似文献
12.
Based on a modified line search scheme, this paper presents a new derivative-free projection method for solving nonlinear monotone equations with convex constraints, which can be regarded as an extension of the scaled conjugate gradient method and the projection method. Under appropriate conditions, the global convergence and linear convergence rate of the proposed method is proven. Preliminary numerical results are also reported to show that this method is promising. 相似文献
13.
In this paper, we propose two derivative-free iterative methods for solving nonlinear monotone equations, which combines two modified HS methods with the projection method in Solodov and Svaiter (1998) [5]. The proposed methods can be applied to solve nonsmooth equations. They are suitable to large-scale equations due to their lower storage requirement. Under mild conditions, we show that the proposed methods are globally convergent. The reported numerical results show that the methods are efficient. 相似文献
14.
Min Zhang Deren Han Gang Qian Xihong Yan 《Journal of Optimization Theory and Applications》2012,152(3):675-695
We propose a new decomposition method for solving a class of monotone variational inequalities with linear constraints. The
proposed method needs only to solve a well-conditioned system of nonlinear equations, which is much easier than a variational
inequality, the subproblem in the classic alternating direction methods. To make the method more flexible and practical, we
solve the sub-problems approximately. We adopt a self-adaptive rule to adjust the parameter, which can improve the numerical
performance of the algorithm. Under mild conditions, the underlying mapping be monotone and the solution set of the problem
be nonempty, we prove the global convergence of the proposed algorithm. Finally, we report some preliminary computational
results, which demonstrate the promising performance of the new algorithm. 相似文献
15.
Igor Boglaev 《Numerical Algorithms》2013,64(4):607-631
This paper deals with a monotone iterative method for solving nonlinear singularly perturbed parabolic problems. Monotone sequences, based on the method of upper and lower solutions, are constructed for a nonlinear difference scheme which approximates the nonlinear parabolic problem. This monotone convergence leads to the existence-uniqueness theorem. The monotone sequences possess quadratic convergence rate. An analysis of uniform convergence of the monotone iterative method to the solutions of the nonlinear difference scheme and to the continuous problem is given. Numerical experiments are presented. 相似文献
16.
A convexification method for a class of global optimization problems with applications to reliability optimization 总被引:1,自引:0,他引:1
A convexification method is proposed for solving a class of global optimization problems with certain monotone properties. It is shown that this class of problems can be transformed into equivalent concave minimization problems using the proposed convexification schemes. An outer approximation method can then be used to find the global solution of the transformed problem. Applications to mixed-integer nonlinear programming problems arising in reliability optimization of complex systems are discussed and satisfactory numerical results are presented. 相似文献
17.
一类求解单调变分不等式的隐式方法 总被引:6,自引:0,他引:6
1.引言变分不等式是一个非常有趣。非常困难的数学问题["].它具有广泛的应用(例如,数学规划中的许多基本问题都可以归结为一个变分不等式问题),因而得到深入的研究并有了不少算法[1,2,5-8,17-21].对线性单调变分不等式,我们最近提出了一系列投影收缩算法Ig-13].本文考虑求解单调变分不等式其中0CW是一闭凸集,F是从正p到自身的一个单调算子,一即有我们用比(·)表示到0上的投影.求解单调变分不等式的一个简单方法是基本投影法[1,6],它的迭代式为然而,如果F不是仿射函数,只有当F一致强单调且LIPSChitZ连续… 相似文献
18.
A. A. Abramov 《Computational Mathematics and Mathematical Physics》2011,51(1):35-39
A modification of the method proposed earlier by the author for solving nonlinear self-adjoint eigenvalue problems for linear
Hamiltonian systems of ordinary differential equations is examined. The basic assumption is that the initial data (that is,
the system matrix and the matrices specifying the boundary conditions) are monotone functions of the spectral parameter. 相似文献
19.
A version of the Dynamical Systems Gradient Method for solving ill-posed nonlinear monotone operator equations is studied
in this paper. A discrepancy principle is proposed and justified. A numerical experiment was carried out with the new stopping
rule. Numerical experiments show that the proposed stopping rule is efficient. Equations with monotone operators are of interest
in many applications.
相似文献
20.
Igor Boglaev 《Journal of Computational and Applied Mathematics》2011,235(12):3541-3553
This paper deals with discrete monotone iterative methods for solving semilinear singularly perturbed parabolic problems. Monotone sequences, based on the accelerated monotone iterative method, are constructed for a nonlinear difference scheme which approximates the semilinear parabolic problem. This monotone convergence leads to the existence-uniqueness theorem. An analysis of uniform convergence of the monotone iterative method to the solutions of the nonlinear difference scheme and continuous problem is given. Numerical experiments are presented. 相似文献