一种非单调自适应信赖域法
A Nonmonotonic Self-Adaptive Trust Region Algorithm

作者: 杭 丹 :空军勤务学院基础部; 王晓燕 , 郝建忠 * , 王 娅 :;

关键词: 无约束最优化信赖域固定步长非单调技术全局收敛性 Unconstrained Optimization Trust Region Fixed Stepsize Nonmonotonic Technique Global Convergence

摘要:
求解无约束优化问题,本文给出了一种改进的非单调信赖域算法。采用了非单调技术,当试探步不被接受时,下一步的迭代步长由一个固定公式给出。并直接给出调整信赖域半径公式数值试验结果表明新算法的有效性。在适当的条件下,证明了算法的全局收敛性。

Abstract:
We propose an improved nonmonotonic trust region algorithm. Our method is to use the nonmonotone technique and if the trial step is rejected, the stepsize is computed by a fixed formula. The trust region radius is updated at a variable rate. Numerical experiment results show that the new algorithm is effective. Under mild conditions, we prove that the algorithm is global convergence.

文章引用: 杭 丹 , 王晓燕 , 郝建忠 , 王 娅 (2013) 一种非单调自适应信赖域法。 理论数学, 3, 312-316. doi: 10.12677/PM.2013.35048

参考文献

[1] Long Hei, A self-adaptive trust regional gorithm, Journal of Computational Mathematics, 2003, 21: 229-236.

[2] J. Nocedal, Y. Yuan, Combing trust region and line search techniques. In: Y. Yuan, Ed., Advances in Nonlinear Programming, Kluver: Springer, 1998: 153-175.

[3] J. T. Mo, K. Zhang and Z. X. Wei. A nonmonotone trust region method for unconstrained optimization. Applied Mathematics and Computation, 2005, 171(1): 371-384.

[4] L. Grippo, F. Lampariello and S. Lucidi. A nonmonotonic line search technique for Newton’s method. SIAM Journal on Numerical Analy- sis, 1986, 23(4): 707-716.

[5] J. J. Mor, B. S. Garbow and K. E. Hillstrom. Testing unconstrained optimization software. ACM Transactions on Mathematical Software, 1981, 7(1): 17-41.

分享
Top