期刊文献+
共找到393篇文章
< 1 2 20 >
每页显示 20 50 100
A Nonmonotone Trust Region Method for Solving Symmetric Nonlinear Equations 被引量:3
1
作者 YUAN Gong-lin WEI Zeng-xin LU Xi-wen 《Chinese Quarterly Journal of Mathematics》 CSCD 2009年第4期574-584,共11页
A trust region method combining with nonmonotone technique is proposed tor solving symmetric nonlinear equations. The global convergence of the given method will be established under suitable conditions. Numerical res... A trust region method combining with nonmonotone technique is proposed tor solving symmetric nonlinear equations. The global convergence of the given method will be established under suitable conditions. Numerical results show that the method is interesting for the given problems. 展开更多
关键词 trust region method nonlinear equations nonmonotone technique
下载PDF
A TRUST REGION METHOD WITH A CONIC MODEL FOR NONLINEARLY CONSTRAINED OPTIMIZATION 被引量:1
2
作者 Wang Chengjing 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2006年第3期263-275,共13页
Trust region methods are powerful and effective optimization methods. The conic model method is a new type of method with more information available at each iteration than standard quadratic-based methods. The adva... Trust region methods are powerful and effective optimization methods. The conic model method is a new type of method with more information available at each iteration than standard quadratic-based methods. The advantages of the above two methods can be combined to form a more powerful method for constrained optimization. The trust region subproblem of our method is to minimize a conic function subject to the linearized constraints and trust region bound. At the same time, the new algorithm still possesses robust global properties. The global convergence of the new algorithm under standard conditions is established. 展开更多
关键词 trust region method conic model constrained optimization nonlinear programming.
下载PDF
A New Nonmonotone Adaptive Trust Region Method 被引量:1
3
作者 Yang Zhang Quanming Ji Qinghua Zhou 《Journal of Applied Mathematics and Physics》 2021年第12期3102-3114,共13页
The trust region method plays an important role in solving optimization problems. In this paper, we propose a new nonmonotone adaptive trust region method for solving unconstrained optimization problems. Actually, we ... The trust region method plays an important role in solving optimization problems. In this paper, we propose a new nonmonotone adaptive trust region method for solving unconstrained optimization problems. Actually, we combine a popular nonmonotone technique with an adaptive trust region algorithm. The new ratio to adjusting the next trust region radius is different from the ratio in the traditional trust region methods. Under some appropriate conditions, we show that the new algorithm has good global convergence and superlinear convergence. 展开更多
关键词 Unconstrained Optimization trust region method Nonmonotone Technique Global Convergence Superlinear Convergence
下载PDF
A CLASS OF TRUST REGION METHODS FOR LINEAR INEQUALITY CONSTRAINED OPTIMIZATION AND ITS THEORY ANALYSIS:I.ALGORITHM AND GLOBAL CONVERGENCEXIU NAIHUA
4
作者 XIU NAIHUA 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 1995年第3期287-296,共10页
A class of trust region methods for solving linear inequality constrained problems is proposed in this paper. It is shown that the algorithm is of global convergence.The algorithm uses a version of the two-sided proje... A class of trust region methods for solving linear inequality constrained problems is proposed in this paper. It is shown that the algorithm is of global convergence.The algorithm uses a version of the two-sided projection and the strategy of the unconstrained trust region methods. It keeps the good convergence properties of the unconstrained case and has the merits of the projection method. In some sense, our algorithm can be regarded as an extension and improvement of the projected type algorithm. 展开更多
关键词 Linear inequality constrained optimization trust region method global convergence
下载PDF
A TRUST REGION METHOD FOR MICROWAVE TOMOGRAPHY 被引量:1
5
作者 Gong Xing (Dept. of Biomedical Engineering, Zhejiang University, Hangzhou 310027) 《Journal of Electronics(China)》 2001年第2期181-184,共4页
A trust region method is proposed to solve the problem of microwave tomography,which is very difficult to be solved for its ill-posedness and nonlinearity. Compared with the Levenberg-Marquardt method, this method int... A trust region method is proposed to solve the problem of microwave tomography,which is very difficult to be solved for its ill-posedness and nonlinearity. Compared with the Levenberg-Marquardt method, this method introduces more a priori knowledge and might obtain better results, though the two methods are equal in some cases. 展开更多
关键词 MICROWAVE TOMOGRAPHY IMAGE RECONSTRUCTION trust region method
下载PDF
A NONMONOTONE TRUST REGION METHOD FOR NONLINEAR LEAST SQUARES PROBLEMS
6
作者 邓乃扬 肖奕 +1 位作者 周方俊 吴育华 《Numerical Mathematics A Journal of Chinese Universities(English Series)》 SCIE 1994年第1期33-53,共21页
In this paper we present a nonmonotone trust region method for nonlinear least squares problems with zero-residual and prove its convergence properties. The extensive numerical results are reported which show that the... In this paper we present a nonmonotone trust region method for nonlinear least squares problems with zero-residual and prove its convergence properties. The extensive numerical results are reported which show that the nonmonotone trust region method is generally superior to the usual trust region method. 展开更多
关键词 trust region method NONLINEAR least SQUARES NONMONOTONE method.
下载PDF
A Non-Monotone Trust Region Method with Non-Monotone Wolfe-Type Line Search Strategy for Unconstrained Optimization
7
作者 Changyuan Li Qinghua Zhou Xiao Wu 《Journal of Applied Mathematics and Physics》 2015年第6期707-712,共6页
In this paper, we propose and analyze a non-monotone trust region method with non-monotone line search strategy for unconstrained optimization problems. Unlike the traditional non-monotone trust region method, our alg... In this paper, we propose and analyze a non-monotone trust region method with non-monotone line search strategy for unconstrained optimization problems. Unlike the traditional non-monotone trust region method, our algorithm utilizes non-monotone Wolfe line search to get the next point if a trial step is not adopted. Thus, it can reduce the number of solving sub-problems. Theoretical analysis shows that the new proposed method has a global convergence under some mild conditions. 展开更多
关键词 UNCONSTRAINED Optimization Non-Monotone trust region method Non-Monotone Line Search Global Convergence
下载PDF
CURVILINEAR PATHS AND TRUST REGION METHODS WITH NONMONOTONIC BACK TRACKING TECHNIQUE FOR UNCONSTRAINED OPTIMIZATION 被引量:26
8
作者 De-tong Zhu (Department of Mathematics, Shanghai Normal University, Shanghai 200234, China) 《Journal of Computational Mathematics》 SCIE EI CSCD 2001年第3期241-258,共18页
Focuses on a study which examined the modification of type approximate trust region methods via two curvilinear paths for unconstrained optimization. Properties of the curvilinear paths; Description of a method which ... Focuses on a study which examined the modification of type approximate trust region methods via two curvilinear paths for unconstrained optimization. Properties of the curvilinear paths; Description of a method which combines line search technique with an approximate trust region algorithm; Information on the convergence analysis; Details on the numerical experiments. 展开更多
关键词 curvilinear paths trust region methods nonmonotonic technique unconstrained optimization
原文传递
AN ADAPTIVE NONMONOTONIC TRUST REGION METHOD WITH CURVILINEAR SEARCHES 被引量:7
9
作者 Qun-yan Zhou Wen-yu Sun 《Journal of Computational Mathematics》 SCIE CSCD 2006年第6期761-770,共10页
In this paper, an algorithm for unconstrained optimization that employs both trust region techniques and curvilinear searches is proposed. At every iteration, we solve the trust region subproblem whose radius is gener... In this paper, an algorithm for unconstrained optimization that employs both trust region techniques and curvilinear searches is proposed. At every iteration, we solve the trust region subproblem whose radius is generated adaptively only once. Nonmonotonic backtracking curvilinear searches are performed when the solution of the subproblem is unacceptable. The global convergence and fast local convergence rate of the proposed algorithms are established under some reasonable conditions. The results of numerical 'experiments are reported to show the effectiveness of the proposed algorithms. 展开更多
关键词 Unconstrained optimization Preconditioned gradient path trust region method Curvilinear search.
原文传递
An improved trust region method for unconstrained optimization 被引量:5
10
作者 ZHOU QingHua ZHANG YaRui +2 位作者 XU FengXia GENG Yan SUN XiaoDian 《Science China Mathematics》 SCIE 2013年第2期425-434,共10页
In this paper,we propose an improved trust region method for solving unconstrained optimization problems.Different with traditional trust region methods,our algorithm does not resolve the subproblem within the trust r... In this paper,we propose an improved trust region method for solving unconstrained optimization problems.Different with traditional trust region methods,our algorithm does not resolve the subproblem within the trust region centered at the current iteration point,but within an improved one centered at some point located in the direction of the negative gradient,while the current iteration point is on the boundary set.We prove the global convergence properties of the new improved trust region algorithm and give the computational results which demonstrate the effectiveness of our algorithm. 展开更多
关键词 unconstrained optimization trust region methods global convergence negative gradient direction ITERATIVE
原文传递
Nonmonotone adaptive trust region method based on simple conic model for unconstrained optimization 被引量:3
11
作者 Lijuan ZHAO Wenyu SUN Raimundo J. B. de SAMPAIO 《Frontiers of Mathematics in China》 SCIE CSCD 2014年第5期1211-1238,共28页
We propose a nonmonotone adaptive trust region method based on simple conic model for unconstrained optimization. Unlike traditional trust region methods, the subproblem in our method is a simple conic model, where th... We propose a nonmonotone adaptive trust region method based on simple conic model for unconstrained optimization. Unlike traditional trust region methods, the subproblem in our method is a simple conic model, where the Hessian of the objective function is approximated by a scalar matrix. The trust region radius is adjusted with a new self-adaptive adjustment strategy which makes use of the information of the previous iteration and current iteration. The new method needs less memory and computational efforts. The global convergence and Q-superlinear convergence of the algorithm are established under the mild conditions. Numerical results on a series of standard test problems are reported to show that the new method is effective and attractive for large scale unconstrained optimization problems. 展开更多
关键词 Nonmonotone technique conic model trust region method largescale optimization global convergence
原文传递
A GLOBALLY AND SUPERLINEARLY CONVERGENT TRUST REGION METHOD FOR LC^1 OPTIMIZATION PROBLEMS 被引量:1
12
作者 Zhang Liping Lai Yanlian Institute of Applied Mathematics,Academia Sinica,Beijing 100080. 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2001年第1期72-80,共9页
A new trust region algorithm for solving convex LC 1 optimization problem is presented.It is proved that the algorithm is globally convergent and the rate of convergence is superlinear under some reasonable assum... A new trust region algorithm for solving convex LC 1 optimization problem is presented.It is proved that the algorithm is globally convergent and the rate of convergence is superlinear under some reasonable assumptions. 展开更多
关键词 LC 1 optimization problem global and superlinear convergence trust region method.
下载PDF
AN AFFINE SCALING DERIVATIVE-FREE TRUST REGION METHOD WITH INTERIOR BACKTRACKING TECHNIQUE FOR BOUNDED-CONSTRAINED NONLINEAR PROGRAMMING 被引量:1
13
作者 GAO Jing ZHU Detong 《Journal of Systems Science & Complexity》 SCIE EI CSCD 2014年第3期537-564,共28页
This paper proposes an arlene scaling derivative-free trust region method with interior backtracking technique for bounded-constrained nonlinear programming. This method is designed to get a stationary point for such ... This paper proposes an arlene scaling derivative-free trust region method with interior backtracking technique for bounded-constrained nonlinear programming. This method is designed to get a stationary point for such a problem with polynomial interpolation models instead of the objective function in trust region subproblem. Combined with both trust region strategy and line search technique, at each iteration, the affine scaling derivative-free trust region subproblem generates a backtracking direction in order to obtain a new accepted interior feasible step. Global convergence and fast local convergence properties are established under some reasonable conditions. Some numerical results are also given to show the effectiveness of the proposed algorithm. 展开更多
关键词 Affine scaling backtracking technique box constrains derivative-free optimization non-linear programming trust region method.
原文传递
AN ADAPTIVE TRUST REGION METHOD FOR EQUALITY CONSTRAINED OPTIMIZATION 被引量:1
14
作者 ZHANGJuliang ZHANGXiangstm ZHUOXinjian 《Journal of Systems Science & Complexity》 SCIE EI CSCD 2003年第4期494-505,共12页
In this paper, a trust region method for equality constrained optimizationbased on nondifferentiable exact penalty is proposed. In this algorithm, the trail step ischaracterized by computation of its normal component ... In this paper, a trust region method for equality constrained optimizationbased on nondifferentiable exact penalty is proposed. In this algorithm, the trail step ischaracterized by computation of its normal component being separated from computation of itstangential component, i.e., only the tangential component of the trail step is constrained by trustradius while the normal component and trail step itself have no constraints. The other maincharacteristic of the algorithm is the decision of trust region radius. Here, the decision of trustregion radius uses the information of the gradient of objective function and reduced Hessian.However, Maratos effect will occur when we use the nondifferentiable exact penalty function as themerit function. In order to obtain the superlinear convergence of the algorithm, we use the twiceorder correction technique. Because of the speciality of the adaptive trust region method, we usetwice order correction when p = 0 (the definition is as in Section 2) and this is different from thetraditional trust region methods for equality constrained optimization. So the computation of thealgorithm in this paper is reduced. What is more, we can prove that the algorithm is globally andsuperlinearly convergent. 展开更多
关键词 equality constrained optimization global convergence trust region method superlinear convergence nondifferentiable exact penalty function maratos effect
原文传递
A SMOOTHING TRUST REGION METHOD FOR NCPS BASED ON THE SMOOTHING GENERALIZED FISCHER-BURMEISTER FUNCTION
15
作者 Xuebin Wang Changfeng Ma Meiyan Li 《Journal of Computational Mathematics》 SCIE CSCD 2011年第3期261-286,共26页
Based on a reformulation of the complementarity problem as a system of nonsmooth equations by using the generMized Fischer-Burmeister function, a smoothing trust re- gion Mgorithm with line search is proposed for solv... Based on a reformulation of the complementarity problem as a system of nonsmooth equations by using the generMized Fischer-Burmeister function, a smoothing trust re- gion Mgorithm with line search is proposed for solving general (not necessarily monotone) nonlinear complementarity problems. Global convergence and, under a nonsingularity assumption, local Q-superlinear/Q-quadratic convergence of the algorithm are established. In particular, it is proved that a unit step size is always accepted after a finite number of iterations. Numerical results also confirm the good theoretical properties of our approach. 展开更多
关键词 Nonlinear complementarity problem Smoothing method trust region method Global convergence Local superlinear convergence.
原文传递
Projected gradient trust-region method for solving nonlinear systems with convex constraints
16
作者 JIA Chun-xia ZHU De-tong 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2011年第1期57-69,共13页
In this paper, a projected gradient trust region algorithm for solving nonlinear equality systems with convex constraints is considered. The global convergence results are developed in a very general setting of comput... In this paper, a projected gradient trust region algorithm for solving nonlinear equality systems with convex constraints is considered. The global convergence results are developed in a very general setting of computing trial directions by this method combining with the line search technique. Close to the solution set this method is locally Q-superlinearly convergent under an error bound assumption which is much weaker than the standard nonsingularity condition. 展开更多
关键词 Nonlinear equation trust region method projected gradient local error bound.
下载PDF
CONIC TRUST REGION METHOD FOR LINEARLY CONSTRAINED OPTIMIZATION
17
作者 Wen-yuSun Jin-yunYuan Ya-xiangYuan 《Journal of Computational Mathematics》 SCIE EI CSCD 2003年第3期295-304,共10页
In this paper we present a trust region method of conic model for linearly constrained optimization problems. We discuss trust region approaches with conic model subproblems. Some equivalent variation properties and o... In this paper we present a trust region method of conic model for linearly constrained optimization problems. We discuss trust region approaches with conic model subproblems. Some equivalent variation properties and optimality conditions are given. A trust region algorithm based on conic model is constructed. Global convergence of the method is established. 展开更多
关键词 trust region method Conic model Constrained optimization.
原文传递
A randomized nonmonotone adaptive trust region method based on the simulated annealing strategy for unconstrained optimization
18
作者 Saman Babaie-Kafaki Saeed Rezaee 《International Journal of Intelligent Computing and Cybernetics》 EI 2019年第3期389-399,共11页
Purpose–The purpose of this paper is to employ stochastic techniques to increase efficiency of the classical algorithms for solving nonlinear optimization problems.Design/methodology/approach–The well-known simulate... Purpose–The purpose of this paper is to employ stochastic techniques to increase efficiency of the classical algorithms for solving nonlinear optimization problems.Design/methodology/approach–The well-known simulated annealing strategy is employed to search successive neighborhoods of the classical trust region(TR)algorithm.Findings–An adaptive formula for computing the TR radius is suggested based on an eigenvalue analysis conducted on the memoryless Broyden-Fletcher-Goldfarb-Shanno updating formula.Also,a(heuristic)randomized adaptive TR algorithm is developed for solving unconstrained optimization problems.Results of computational experiments on a set of CUTEr test problems show that the proposed randomization scheme can enhance efficiency of the TR methods.Practical implications–The algorithm can be effectively used for solving the optimization problems which appear in engineering,economics,management,industry and other areas.Originality/value–The proposed randomization scheme improves computational costs of the classical TR algorithm.Especially,the suggested algorithm avoids resolving the TR subproblems for many times. 展开更多
关键词 Nonlinear programming Simulated annealing Adaptive radius trust region method Unconstrained optimization
原文传递
A Polynomial Chaos Expansion Trust Region Method for Robust Optimization
19
作者 Samih Zein 《Communications in Computational Physics》 SCIE 2013年第7期412-424,共13页
Robust optimization is an approach for the design of a mechanical structure which takes into account the uncertainties of the design variables.It requires at each iteration the evaluation of some robust measures of th... Robust optimization is an approach for the design of a mechanical structure which takes into account the uncertainties of the design variables.It requires at each iteration the evaluation of some robust measures of the objective function and the constraints.In a previous work,the authors have proposed a method which efficiently generates a design of experiments with respect to the design variable uncertainties to compute the robust measures using the polynomial chaos expansion.This paper extends the proposed method to the case of the robust optimization.The generated design of experiments is used to build a surrogate model for the robust measures over a certain trust region.This leads to a trust region optimization method which only requires one evaluation of the design of experiments per iteration(single loop method).Unlike other single loop methods which are only based on a first order approximation of robust measure of the constraints and which does not handle a robust measure for the objective function,the proposed method can handle any approximation order and any choice for the robust measures.Some numerical experiments based on finite element functions are performed to show the efficiency of the method. 展开更多
关键词 Reliability based design optimization polynomial chaos expansion trust region method
原文传递
An adaptive trust region method and its convergence 被引量:10
20
作者 章祥荪 张菊亮 廖立志 《Science China Mathematics》 SCIE 2002年第5期620-631,共12页
In this paper, a new trust region subproblem is proposed. The trust radius in the new subproblem adjusts itself adaptively. As a result, an adaptive trust region method is constructed based on the new trust region sub... In this paper, a new trust region subproblem is proposed. The trust radius in the new subproblem adjusts itself adaptively. As a result, an adaptive trust region method is constructed based on the new trust region subproblem. The local and global convergence results of the adaptive trust region method are proved.Numerical results indicate that the new method is very efficient. 展开更多
关键词 trust region method UNCONSTRAINED optimization GLOBAL convergence SUPERLINEAR convergence.
原文传递
上一页 1 2 20 下一页 到第
使用帮助 返回顶部