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1.
Zhen-Jun Shi Author Vitae Zhiwei Xu Author Vitae 《Journal of Computational and Applied Mathematics》2009,231(1):365-377
The trust region method is an effective approach for solving optimization problems due to its robustness and strong convergence. However, the subproblem in the trust region method is difficult or time-consuming to solve in practical computation, especially in large-scale problems. In this paper we consider a new class of trust region methods, specifically subspace trust region methods. The subproblem in these methods has an adequate initial trust region radius and can be solved in a simple subspace. It is easier to solve than the original subproblem because the dimension of the subproblem in the subspace is reduced substantially. We investigate the global convergence and convergence rate of these methods. 相似文献
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E. Mijangos 《Journal of Optimization Theory and Applications》2006,128(1):167-190
The minimization of nonlinearly constrained network flow problems can be performed by using approximate subgradient methods.
The idea is to solve this kind of problem by means of primal-dual methods, given that the minimization of nonlinear network
flow problems can be done efficiently exploiting the network structure. In this work, it is proposed to solve the dual problem
by using ε-subgradient methods, as the dual function is estimated by minimizing approximately a Lagrangian function, which
includes the side constraints (nonnetwork constraints) and is subject only to the network constraints. Some well-known subgradient
methods are modified in order to be used as ε-subgradient methods and the convergence properties of these new methods are
analyzed. Numerical results appear very promising and effective for this kind of problems
This research was partially supported by Grant MCYT DPI 2002-03330. 相似文献
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《European Journal of Operational Research》2003,151(2):415-433
This paper deals with performance evaluation and scheduling problems in m machine stochastic flow shop with unlimited buffers. The processing time of each job on each machine is a random variable exponentially distributed with a known rate. We consider permutation flow shop. The objective is to find a job schedule which minimizes the expected makespan. A classification of works about stochastic flow shop with random processing times is first given. In order to solve the performance evaluation problem, we propose a recursive algorithm based on a Markov chain to compute the expected makespan and a discrete event simulation model to evaluate the expected makespan. The recursive algorithm is a generalization of a method proposed in the literature for the two machine flow shop problem to the m machine flow shop problem with unlimited buffers. In deterministic context, heuristics (like CDS [Management Science 16 (10) (1970) B630] and Rapid Access [Management Science 23 (11) (1977) 1174]) and metaheuristics (like simulated annealing) provide good results. We propose to adapt and to test this kind of methods for the stochastic scheduling problem. Combinations between heuristics or metaheuristics and the performance evaluation models are proposed. One of the objectives of this paper is to compare the methods together. Our methods are tested on problems from the OR-Library and give good results: for the two machine problems, we obtain the optimal solution and for the m machine problems, the methods are mutually validated. 相似文献
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A trust region-CG algorithm for deblurring problem in atmospheric image reconstruction 总被引:3,自引:0,他引:3
In this paper we solve large scale ill-posed problems, particularly the image restoration problem in atmospheric imaging sciences,
by a trust region-CG algorithm. Image restoration involves the removal or minimization of degradation (blur, clutter, noise,
etc.) in an image using a priori knowledge about the degradation phenomena. Our basic technique is the so-called trust region
method, while the subproblem is solved by the truncated conjugate gradient method, which has been well developed for well-posed
problems. The trust region method, due to its robustness in global convergence, seems to be a promising way to deal with ill-posed
problems. 相似文献
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有理函数积分的公式解法 总被引:2,自引:1,他引:1
被积函数为有理函数的不定积分求解通常是采用待定系数法。本文提出了这类积分的非待定系数公式解法,较完美地解决了这类积分问题。在实际应用中显示了这种新型方法是简捷的和有效的。它的优点还在于不仅对一些常规方法极为困难或无法解决的问题给以简明的解,而且借助于电子计算机可解决更复杂的问题。 相似文献
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Hideaki Iiduka 《Applied mathematics and computation》2011,217(13):6315-6327
Many constrained sets in problems such as signal processing and optimal control can be represented as a fixed point set of a certain nonexpansive mapping, and a number of iterative algorithms have been presented for solving a convex optimization problem over a fixed point set. This paper presents a novel gradient method with a three-term conjugate gradient direction that is used to accelerate conjugate gradient methods for solving unconstrained optimization problems. It is guaranteed that the algorithm strongly converges to the solution to the problem under the standard assumptions. Numerical comparisons with the existing gradient methods demonstrate the effectiveness and fast convergence of this algorithm. 相似文献
9.
Chengjin Li 《Journal of Optimization Theory and Applications》2014,163(2):569-594
The matrix rank minimization problem is widely applied in many fields such as control, signal processing and system identification. However, the problem is NP-hard in general and is computationally hard to directly solve in practice. In this paper, we provide a new approximation function of the matrix rank function, and the corresponding approximation problems can be used to approximate the matrix rank minimization problem within any level of accuracy. Furthermore, the successive projected gradient method, which is designed based on the monotonicity and the Fréchet derivative of these new approximation function, can be used to solve the matrix rank minimization this problem by using the projected gradient method to find the stationary points of a series of approximation problems. Finally, the convergence analysis and the preliminary numerical results are given. 相似文献
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电力系统中地网腐蚀诊断的一种新的数学模型及其仿真计算 总被引:1,自引:0,他引:1
对电力系统中具有重大应用价值的地网腐蚀诊断问题抽象出仿真求解的一种新的数学模型:即求解带约束的非线性隐式方程组模型.但由于问题本身的物理特性决定了所建立的数学模型具有以下特点:一是非线性方程组为欠定方程组,而且非线性程度非常高;二是方程组的所有函数均为隐函数;三是方程组附加若干箱约束条件.这种特性给模型分析与算法设计带来巨大困难.对于欠定方程组的求解,文中根据工程实际背景,尽可能地扩充方程的个数,使之成为超定方程组,然后对欠定方程组和超定方程组分别求解并进行比较.将带约束的非线性隐函数方程组求解问题,转化为无约束非线性最小二乘问题,并采用矩阵求导等技术和各种算法设计技巧克服隐函数的计算困难,最后使用拟牛顿信赖域方法进行计算.大量的计算实例表明,文中所提出的数学模型及求解方法是可行的.与目前广泛采用的工程简化模型相比较,在模型和算法上具有很大优势. 相似文献
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El-Sayed M. E. Mostafa 《Numerical Functional Analysis & Optimization》2013,34(6):591-610
In this article, we consider the static output feedback problem for discrete-time systems when complete set of state variables is not available. It has been reported that quasi-Newton methods have substandard performance on this problem. A structured quasi-Newton method with trust region globalization is analyzed and studied for solving this problem. Moreover, the classical Anderson-Moore method is enhanced by using the trust region mechanism to ensure global convergence instead of the line search technique. The algorithms are tested numerically on test problems of engineering applications. 相似文献
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Rachel Minster Irina Viviano Xiaotian Liu Grey Ballard 《Numerical Linear Algebra with Applications》2023,30(6):e2511
The CP tensor decomposition is used in applications such as machine learning and signal processing to discover latent low-rank structure in multidimensional data. Computing a CP decomposition via an alternating least squares (ALS) method reduces the problem to several linear least squares problems. The standard way to solve these linear least squares subproblems is to use the normal equations, which inherit special tensor structure that can be exploited for computational efficiency. However, the normal equations are sensitive to numerical ill-conditioning, which can compromise the results of the decomposition. In this paper, we develop versions of the CP-ALS algorithm using the QR decomposition and the singular value decomposition, which are more numerically stable than the normal equations, to solve the linear least squares problems. Our algorithms utilize the tensor structure of the CP-ALS subproblems efficiently, have the same complexity as the standard CP-ALS algorithm when the input is dense and the rank is small, and are shown via examples to produce more stable results when ill-conditioning is present. Our MATLAB implementation achieves the same running time as the standard algorithm for small ranks, and we show that the new methods can obtain lower approximation error. 相似文献
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解线性约束优化问题的新锥模型信赖域法 总被引:1,自引:0,他引:1
本文提出了一个解线性等式约束优化问题的新锥模型信赖域方法.论文采用零空间技术消除了新锥模型子问题中的线性等式约束,用折线法求解转换后的子问题,并给出了解线性等式约束优化问题的信赖域方法.论文提出并证明了该方法的全局收敛性,并给出了该方法解线性等式约束优化问题的数值实验.理论和数值实验结果表明新锥模型信赖域方法是有效的,这给出了用新锥模型进一步研究非线性优化的基础. 相似文献
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In this paper, we propose two compact finite difference approximations for three-dimensional biharmonic equation with Dirichlet boundary conditions of second kind. In these methods there is no need to define special formulas near the boundaries and boundary conditions are incorporated with these techniques. The unknown solution and its second derivatives are carried as unknowns at grid points. We derive second-order and fourth-order approximations on a 27 point compact stencil. Classical iteration methods such as Gauss–Seidel and SOR for solving the linear system arising from the second-order and fourth-order discretisation suffer from slow convergence. In order to overcome this problem we use multigrid method which exhibit grid-independent convergence and solve the linear system of equations in small amount of computer time. The fourth-order finite difference approximations are used to solve several test problems and produce high accurate numerical solutions. 相似文献
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A globally convergent trust region algorithm for optimization with general constraints and simple bounds 总被引:3,自引:0,他引:3
1.IntroductionInthispaper,weconsiderthefollowingnonlinearprogr~ngproblemwherec(x)=(c,(x),c2(2),',We(.))',i(x)andci(x)(i=1,2,',m)arerealfunctions*ThisworkissupPOrtedbytheNationalNaturalScienceFOundationofChinaandtheManagement,DecisionandinformationSystemLab,theChineseAcademyofSciences.definedinD={xEReIISx5u}.Weassumethath相似文献
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Minimizing of total tardiness is one of the most studied topics on single machine problems. Researchers develop a number of optimizing and heuristic methods to solve this NP-hard problem. In this paper, the problem of minimizing total tardiness is examined in a learning effect situation. The concept of learning effects describes the reduction of processing times arising from process repetition. A 0–1 integer programming model is developed to solve the problem. Also, a random search, the tabu search and the simulated annealing-based methods are proposed for the problem and the solutions of the large size problems with up to 1000 jobs are found by these methods. To the best of our knowledge, no works exists on the total tardiness problem with a learning effect tackled in this paper. 相似文献
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Ekkehard W. Sachs 《Annals of Operations Research》1990,27(1):311-341
Infinite-dimensional optimization problems occur in various applications such as optimal control problems and parameter identification problems. If these problems are solved numerically the methods require a discretization which can be viewed as a perturbation of the data of the optimization problem. In this case the expected convergence behavior of the numerical method used to solve the problem does not only depend on the discretized problem but also on the original one. Algorithms which are analyzed include the gradient projection method, conditional gradient method, Newton's method and quasi-Newton methods for unconstrained and constrained problems with simple constraints. 相似文献
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This article considers the bilevel linear programming problem with interval coefficients in both objective functions. We propose a cutting plane method to solve such a problem. In order to obtain the best and worst optimal solutions, two types of cutting plane methods are developed based on the fact that the best and worst optimal solutions of this kind of problem occur at extreme points of its constraint region. The main idea of the proposed methods is to solve a sequence of linear programming problems with cutting planes that are successively introduced until the best and worst optimal solutions are found. Finally, we extend the two algorithms proposed to compute the best and worst optimal solutions of the general bilevel linear programming problem with interval coefficients in the objective functions as well as in the constraints. 相似文献