共查询到20条相似文献,搜索用时 15 毫秒
1.
Augmented Lagrangian Homotopy Method for the Regularization of Total Variation Denoising Problems 总被引:1,自引:0,他引:1
L. A. Melara A. J. Kearsley R. A. Tapia 《Journal of Optimization Theory and Applications》2007,134(1):15-25
This paper presents a homotopy procedure which improves the solvability of mathematical programming problems arising from
total variational methods for image denoising. The homotopy on the regularization parameter involves solving a sequence of
equality-constrained optimization problems where the positive regularization parameter in each optimization problem is initially
large and is reduced to zero. Newton’s method is used to solve the optimization problems and numerical results are presented. 相似文献
2.
3.
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
4.
崔颖川 《高等学校计算数学学报》1999,21(1):71-80
1引言设H为一给定的n×n对称矩阵,cR",本文考虑如}的约束优化问题这里a>0为给定的参数,C={xRnx<a是R”中的一个球体,K是一个简单凸闭集.当K=Rn时,问题(P)便是无约束优化的信赖域子问题.当K={xRnμ≤x≤υ5,(μ1,μ2,…,μn)T,υ=(υ1,υ2…,υn)T,且—∞<μi<υi<v<+∞,i=1,2,…,n时,问题(P)便是用信赖域方法求解带上下界约束的优化问题时遇到的子问题.对于无约束信赖域方法的子问题已经有了比较成熟的算法[8,12-13,15-16].K=R… 相似文献
5.
The aim of this paper is to propose a variational piecewise constant level set method for solving elliptic shape and topology optimization problems. The original model is approximated by a two-phase optimal shape design problem by the ersatz material approach. Under the piecewise constant level set framework, we first reformulate the two-phase design problem to be a new constrained optimization problem with respect to the piecewise constant level set function. Then we solve it by the projection Lagrangian method. A gradient-type iterative algorithm is presented. Comparisons between our numerical results and those obtained by level set approaches show the effectiveness, accuracy and efficiency of our algorithm. 相似文献
6.
本文以弹性力学中的摩擦问题为背景,采用多重互易方法(MRM方法),边界元方法,将摩擦问题中的第二类混合变分不等式化解为MRM-边界混合变分不等式,给出了MRM-边界混合变分不等式解的存在唯—性,通过引入变换将原MRM-边界混合变分不等式化解为标准的凸极值问题,采用正则化方法处理后,给出了MRM-边界混合变分不等式的迭代分解方法。文末给出了数值算例。 相似文献
7.
On the coupling of regularization techniques and the boundary element method for a hemivariational inequality modelling a delamination problem
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Nina Ovcharova 《Mathematical Methods in the Applied Sciences》2017,40(1):60-77
In this paper, we couple regularization techniques of nondifferentiable optimization with the h‐version of the boundary element method (h‐BEM) to solve nonsmooth variational problems arising in contact mechanics. As a model example, we consider the delamination problem. The variational formulation of this problem leads to a hemivariational inequality with a nonsmooth functional defined on the contact boundary. This problem is first regularized and then discretized by an h‐BEM. We prove convergence of the h‐BEM Galerkin solution of the regularized problem in the energy norm, provide an a priori error estimate and give a numerical examples. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
8.
Shih-Hsiang Chang 《Journal of Computational and Applied Mathematics》2010,234(10):3043-5565
Troesch’s problem is an inherently unstable two-point boundary value problem. A new and efficient algorithm based on the variational iteration method and variable transformation is proposed to solve Troesch’s problem. The underlying idea of the method is to convert the hyperbolic-type nonlinearity in the problem into polynomial-type nonlinearities by variable transformation, and the variational iteration method is then directly used to solve this transformed problem. Only the second-order iterative solution is required to provide a highly accurate analytical solution as compared with those obtained by other analytical and numerical methods. 相似文献
9.
In this paper, we consider a vector optimization problem involving approximately star-shaped functions. We formulate approximate vector variational inequalities in terms of Fréchet subdifferentials and solve the vector optimization problem. Under the assumptions of approximately straight functions, we establish necessary and sufficient conditions for a solution of approximate vector variational inequality to be an approximate efficient solution of the vector optimization problem. We also consider the corresponding weak versions of the approximate vector variational inequalities and establish various results for approximate weak efficient solutions. 相似文献
10.
本文通过对倒向随机微分方程进行摄动的方法研究了金融市场中最优投资组合和消费选择问题.在没有凸性假设下,用Ekland 变分原理解决了这个带初始约束的优化问题 相似文献
11.
N. H. Sweilam 《Journal of Difference Equations and Applications》2013,19(4):443-460
This paper considers the numerical simulation of optimal control evolution dam problem by using conjugate gradient method.The paper considers the free boundary value problem related to time dependent fluid flow in a homogeneous earth rectangular dam.The dam is taken to be sufficiently long that the flow is considered to be two dimensional.On the left and right walls of the dam there is a reservoir of fluid at a level dependent on time.This problem can be transformed into a variational inequality on a fixed domain.The numerical techniques we use are based on a linear finite element method to approximate the state equations and a conjugate gradient algorithm to solve the discrete optimal control problem.This algorithm is based on Armijo's rule in the unconstrained optimization theory.The convergence of the discrete optimal solutions to the continuous optimal solutions,and the convergence of the conjugate gradient algorithm are proved.A numerical example is given to determine the location of the minimum surface 相似文献
12.
《Optimization》2012,61(2):131-147
The problem of finding a solution to a system of mixed variational inequalities, which can be interpreted as a generalization of a primal–dual formulation of an optimization problem under arbitrary right-hand side perturbations, is considered. A number of various equilibrium type problems are particular cases of this problem. We suggest the problem to be reduced to a class of variational inequalities and propose a general descent type method to find its solution. If the primal cost function does not possess strengthened convexity properties, this descent method can be combined with a partial regularization method. 相似文献
13.
In this paper an ultraspherical integral method is proposed to solve optimal control problems governed by ordinary differential equations. Ultraspherical approximation method reduced the problem to a constrained optimization problem. Penalty leap frog method is presented to solve the resulting constrained optimization problem. Error estimates for the ultraspherical approximations are derived and a technique that gives an optimal approximation of the problems is introduced. Numerical results are included to confirm the efficiency and accuracy of the method. 相似文献
14.
Hideaki Iiduka 《Journal of Optimization Theory and Applications》2011,148(3):580-592
Many practical problems such as signal processing and network resource allocation are formulated as the monotone variational
inequality over the fixed point set of a nonexpansive mapping, and iterative algorithms to solve these problems have been
proposed. This paper discusses a monotone variational inequality with variational inequality constraint over the fixed point
set of a nonexpansive mapping, which is called the triple-hierarchical constrained optimization problem, and presents an iterative
algorithm for solving it. Strong convergence of the algorithm to the unique solution of the problem is guaranteed under certain
assumptions. 相似文献
15.
Salman Jahanshahi Delfim F. M. Torres 《Journal of Optimization Theory and Applications》2017,174(1):156-175
We develop a simple and accurate method to solve fractional variational and fractional optimal control problems with dependence on Caputo and Riemann–Liouville operators. Using known formulas for computing fractional derivatives of polynomials, we rewrite the fractional functional dynamical optimization problem as a classical static optimization problem. The method for classical optimal control problems is called Ritz’s method. Examples show that the proposed approach is more accurate than recent methods available in the literature. 相似文献
16.
Na Zhao 《Applied mathematics and computation》2010,217(7):3368-3378
Many optimization problems can be reformulated as a system of equations. One may use the generalized Newton method or the smoothing Newton method to solve the reformulated equations so that a solution of the original problem can be found. Such methods have been powerful tools to solve many optimization problems in the literature. In this paper, we propose a Newton-type algorithm for solving a class of monotone affine variational inequality problems (AVIPs for short). In the proposed algorithm, the techniques based on both the generalized Newton method and the smoothing Newton method are used. In particular, we show that the algorithm can find an exact solution of the AVIP in a finite number of iterations under an assumption that the solution set of the AVIP is nonempty. Preliminary numerical results are reported. 相似文献
17.
In this paper, we investigate an inverse problem of recovering the zeroth-order coefficient and fractional order simultaneously in a time-fractional reaction-diffusion-wave equation by using boundary measurement data from both of uniqueness and numerical method. We prove the uniqueness of the considered inverse problem and the Lipschitz continuity of the forward operator. Then the inverse problem is formulated into a variational problem by the Tikhonov-type regularization. Based on the continuity of the forward operator, we prove that the minimizer of the Tikhonov-type functional exists and converges to the exact solution under an a priori choice of regularization parameter. The steepest descent method combined with Nesterov acceleration is adopted to solve the variational problem. Three numerical examples are presented to support the efficiency and rationality of our proposed method. 相似文献
18.
L. C. Ceng B. S. Mordukhovich J. C. Yao 《Journal of Optimization Theory and Applications》2010,146(2):267-303
This paper studies a general vector optimization problem of finding weakly efficient points for mappings from Hilbert spaces
to arbitrary Banach spaces, where the latter are partially ordered by some closed, convex, and pointed cones with nonempty
interiors. To find solutions of this vector optimization problem, we introduce an auxiliary variational inequality problem
for a monotone and Lipschitz continuous mapping. The approximate proximal method in vector optimization is extended to develop
a hybrid approximate proximal method for the general vector optimization problem under consideration by combining an extragradient
method to find a solution of the variational inequality problem and an approximate proximal point method for finding a root
of a maximal monotone operator. In this hybrid approximate proximal method, the subproblems consist of finding approximate
solutions to the variational inequality problem for monotone and Lipschitz continuous mapping, and then finding weakly efficient
points for a suitable regularization of the original mapping. We present both absolute and relative versions of our hybrid
algorithm in which the subproblems are solved only approximately. The weak convergence of the generated sequence to a weak
efficient point is established under quite mild assumptions. In addition, we develop some extensions of our hybrid algorithms
for vector optimization by using Bregman-type functions. 相似文献
19.
We know that variational inequality problem is very important in the nonlinear analysis. For a variational inequality problem defined over a nonempty fixed point set of a nonexpansive mapping in Hilbert space, the strong convergence theorem has been proposed by I. Yamada. The algorithm in this theorem is named the hybrid steepest descent method. Based on this method, we propose a new weak convergence theorem for zero points of inverse strongly monotone mapping and fixed points of nonexpansive mapping in Hilbert space. Using this result, we obtain some new weak convergence theorems which are useful in nonlinear analysis and optimization problem. 相似文献
20.
Dinh Nho Hào Nguyen Trung Thành 《Journal of Computational and Applied Mathematics》2009,232(2):361-377
In this paper we consider a multi-dimensional inverse heat conduction problem with time-dependent coefficients in a box, which is well-known to be severely ill-posed, by a variational method. The gradient of the functional to be minimized is obtained by the aid of an adjoint problem, and the conjugate gradient method with a stopping rule is then applied to this ill-posed optimization problem. To enhance the stability and the accuracy of the numerical solution to the problem, we apply this scheme to the discretized inverse problem rather than to the continuous one. The difficulties with large dimensions of discretized problems are overcome by a splitting method which only requires the solution of easy-to-solve one-dimensional problems. The numerical results provided by our method are very good and the techniques seem to be very promising. 相似文献