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1.
In this paper, we present a nonmonotone conic trust region method based on line search technique for unconstrained optimization. The new algorithm can be regarded as a combination of nonmonotone technique, line search technique and conic trust region method. When a trial step is not accepted, the method does not resolve the trust region subproblem but generates an iterative point whose steplength satisfies some line search condition. The function value can only be allowed to increase when trial steps are not accepted in close succession of iterations. The local and global convergence properties are proved under reasonable assumptions. Numerical experiments are conducted to compare this method with the existing methods. 相似文献
2.
Shao-Jian Qu Ke-Cun Zhang Jian Zhang 《Journal of Computational and Applied Mathematics》2008,220(1-2):119-128
In this paper, we present a nonmonotone trust-region method of conic model for unconstrained optimization. The new method combines a new trust-region subproblem of conic model proposed in [Y. Ji, S.J. Qu, Y.J. Wang, H.M. Li, A conic trust-region method for optimization with nonlinear equality and inequality 4 constrains via active-set strategy, Appl. Math. Comput. 183 (2006) 217–231] with a nonmonotone technique for solving unconstrained optimization. The local and global convergence properties are proved under reasonable assumptions. Numerical experiments are conducted to compare this method with the method of [Y. Ji, S.J. Qu, Y.J. Wang, H.M. Li, A conic trust-region method for optimization with nonlinear equality and inequality 4 constrains via active-set strategy, Appl. Math. Comput. 183 (2006) 217–231]. 相似文献
3.
Ying Ji Yijun Li Xinli Zhang 《Journal of Computational and Applied Mathematics》2010,233(8):1746-1754
In this paper, we present a new nonmonotone trust-region method of conic model for solving unconstrained optimization problems. Both the local and global convergence properties are analyzed under reasonable assumptions. Numerical experiments are conducted to compare this method with some existed ones which indicate that the new method is efficient. 相似文献
4.
Lijuan ZHAO Wenyu SUN Raimundo J. B. de SAMPAIO 《Frontiers of Mathematics in China》2014,9(5):1211-1238
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. 相似文献
5.
Wu Qing-jun 《Applied mathematics and computation》2010,217(8):4274-4281
In this paper, a nonmonotone trust region algorithm for unconstrained optimization problems is presented. In the algorithm, a kind of nonmonotone technique, which is evidently different from Grippo, Lampariello and Lucidi’s approach, is used. Under mild conditions, global and local convergence results of the algorithm are established. Preliminary numerical results show that the new algorithm is efficient. 相似文献
6.
Yigui Ou 《Applied Numerical Mathematics》2011,61(7):900-909
This paper presents a hybrid trust region algorithm for unconstrained optimization problems. It can be regarded as a combination of ODE-based methods, line search and trust region techniques. A feature of the proposed method is that at each iteration, a system of linear equations is solved only once to obtain a trial step. Further, when the trial step is not accepted, the method performs an inexact line search along it instead of resolving a new linear system. Under reasonable assumptions, the algorithm is proven to be globally and superlinearly convergent. Numerical results are also reported that show the efficiency of this proposed method. 相似文献
7.
We consider an efficient trust-region framework which employs a new nonmonotone line search technique for unconstrained optimization problems. Unlike the traditional nonmonotone trust-region method, our proposed algorithm avoids resolving the subproblem whenever a trial step is rejected. Instead, it performs a nonmonotone Armijo-type line search in direction of the rejected trial step to construct a new point. Theoretical analysis indicates that the new approach preserves the global convergence to the first-order critical points under classical assumptions. Moreover, superlinear and quadratic convergence are established under suitable conditions. Numerical experiments show the efficiency and effectiveness of the proposed approach for solving unconstrained optimization problems. 相似文献
8.
9.
In this paper, we present a nonmonotone filter trust region algorithm for solving nonlinear equality constrained optimization. Similar to Bryd–Omojokun class of algorithms, each step is composed of a quasi-normal step and a tangential step. This new method has more flexibility for the acceptance of the trial step compared to the filter methods, and requires less computational costs compared with the monotone methods. Under reasonable conditions, we give the globally convergence properties. Numerical tests are presented that confirm the efficiency of the approach. 相似文献
10.
This paper discusses nonlinear complementarity problems; its goal is to present a globally and superlinearly convergent algorithm for the discussed problems. Filter methods are extensively studied to handle nonlinear complementarity problem. Because of good numerical results, filter techniques are attached. By means of a filter strategy, we present a new trust region method based on a conic model for nonlinear complementarity problems. Under a proper condition, the superlinear convergence of the algorithm is established without the strict complementarity condition. 相似文献
11.
The aim of this paper is to incorporate the preconditioned gradient path in a nonmonotone stabilization algorithm for unconstrained optimization. The global convergence and locally superlinear convergence are established for this class of algorithms. Finally, we report in details the numerical results which show the effectiveness of the proposed algorithm. 相似文献
12.
A new trust region method with adaptive radius 总被引:2,自引:0,他引:2
In this paper we develop a new trust region method with adaptive radius for unconstrained optimization problems. The new method
can adjust the trust region radius automatically at each iteration and possibly reduces the number of solving subproblems.
We investigate the global convergence and convergence rate of this new method under some mild conditions. Theoretical analysis
and numerical results show that the new adaptive trust region radius is available and reasonable and the resultant trust region
method is efficient in solving practical optimization problems.
The work was supported in part by NSF grant CNS-0521142, USA. 相似文献
13.
In this paper, we propose a nonmonotone adaptive trust region method for unconstrained optimization problems. This method can produce an adaptive trust region radius automatically at each iteration and allow the functional value of iterates to increase within finite iterations and finally decrease after such finite iterations. This nonmonotone approach and adaptive trust region radius can reduce the number of solving trust region subproblems when reaching the same precision. The global convergence and convergence rate of this method are analyzed under some mild conditions. Numerical results show that the proposed method is effective in practical computation. 相似文献
14.
This paper presents a nonmonotone trust region algorithm for equality constrained optimization problems. Under certain conditions, we obtain not only the global convergence in the sense that every limit point is a stationary point but also the one step superlinear convergence rate. Numerical tests are also given to show the efficiency of the proposed algorithm. 相似文献
15.
Wenyu Sun Liusheng Hou Chuangying Dang 《Computational Optimization and Applications》2008,40(1):59-72
It is well-known that the conjugate gradient method is widely used for solving large scale optimization problems. In this
paper a modified trust-region method with Beale’s Preconditioned Conjugate Gradient (BPCG) technique is developed for solving
unconstrained optimization problems. The modified version adopts an adaptive rule and retains some useful information when
an unsuccessful iteration occurs, and therefore improves the efficiency of the method. The behavior and the convergence properties
are discussed. Some numerical experiments are reported.
This work was partially supported by Grant of the National Natural Science Foundation of China, Grant: 20040319003 of the
Doctoral Site of the Education Ministry of China, and SRG: 7001428 of City University of Hong Kong. 相似文献
16.
Wang Chengjing 《高校应用数学学报(英文版)》2006,21(3):263-275
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. 相似文献
17.
In this paper, we present an adaptive trust region method for solving unconstrained optimization problems which combines nonmonotone technique with a new update rule for the trust region radius. At each iteration, our method can adjust the trust region radius of related subproblem. We construct a new ratio to adjust the next trust region radius which is different from the ratio in the traditional trust region methods. The global and superlinear convergence results of the method are established under reasonable assumptions. Numerical results show that the new method is efficient for unconstrained optimization problems. 相似文献
18.
M.A. Diniz-Ehrhardt J.M. Martínez M. Raydan 《Journal of Computational and Applied Mathematics》2008,219(2):383
A tolerant derivative–free nonmonotone line-search technique is proposed and analyzed. Several consecutive increases in the objective function and also nondescent directions are admitted for unconstrained minimization. To exemplify the power of this new line search we describe a direct search algorithm in which the directions are chosen randomly. The convergence properties of this random method rely exclusively on the line-search technique. We present numerical experiments, to illustrate the advantages of using a derivative-free nonmonotone globalization strategy, with approximated-gradient type methods and also with the inverse SR1 update that could produce nondescent directions. In all cases we use a local variation finite differences approximation to the gradient. 相似文献
19.
《Applied Mathematical Modelling》2014,38(9-10):2601-2612
This study devotes to incorporating a nonmonotone strategy with an automatically adjusted trust-region radius to propose a more efficient hybrid of trust-region approaches for unconstrained optimization. The primary objective of the paper is to introduce a more relaxed trust-region approach based on a novel extension in trust-region ratio and radius. The next aim is to employ stronger nonmonotone strategies, i.e. bigger trust-region ratios, far from the optimizer and weaker nonmonotone strategies, i.e. smaller trust-region ratios, close to the optimizer. The global convergence to first-order stationary points as well as the local superlinear and quadratic convergence rates are also proved under some reasonable conditions. Some preliminary numerical results and comparisons are also reported. 相似文献
20.
A class of nonmonotone trust region algorithms is presented for unconstrained optimizations. Under suitable conditions, the
global and Q-quadratic convergences of the algorithm are proved. Several rules of choosing trial steps and trust region radii
are also discussed.
Project supported by the National Natural Science Foundation of China (Grant No. 19136012). 相似文献