DERIVATIVE-FREE OPTIMIZATION OF NOISY FUNCTIONS VIA QUASI-NEWTON METHODS
DERIVATIVE-FREE OPTIMIZATION OF NOISY FUNCTIONS VIA QUASI-NEWTON METHODS
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DOI：
10.1137/18m1177718
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发表时间：
2019-01-01
影响因子：
3.1
通讯作者：
Nocedal, Jorge
中科院分区：
文献类型：
--
作者：
Berahas, Albert S.;Byrd, Richard H.;Nocedal, Jorge
本文提出了一种求解含噪函数极小化问题的有限差分拟牛顿法。该方法利用了BFGS更新的可伸缩性和能力，并采用了一种自适应过程来基于Hamming的噪声估计技术来选择差分区间h，该噪声估计技术是基于Hamming的噪声估计技术，以及更多[SIAM J.Sci]和Wild[SIAM J.Sci]。计算机，33(2011)，第1292-1314页]。该噪声估计过程和h的选择是廉价的，但并不总是准确的，并且为了防止失败，该算法结合了在线搜索过程不能产生可接受的点的情况下采取适当动作的恢复机制。提出了一种新的收敛分析方法，该方法考虑了噪声线搜索过程的影响。给出了该方法与函数插值信赖域方法的数值实验结果。
This paper presents a finite-difference quasi-Newton method for the minimization of noisy functions. The method takes advantage of the scalability and power of BFGS updating, and employs an adaptive procedure for choosing the differencing interval h based on the noise estimation techniques of Hamming [Introduction to Applied Numerical Analysis, Courier Corporation, North Chelmsford, MA, 2012] and More and Wild [SIAM J. Sci. Comput., 33 (2011), pp. 1292-1314]. This noise estimation procedure and the selection of h are inexpensive but not always accurate, and to prevent failures the algorithm incorporates a recovery mechanism that takes appropriate action in the case when the line-search procedure is unable to produce an acceptable point. A novel convergence analysis is presented that considers the effect of a noisy line-search procedure. Numerical experiments comparing the method to a function interpolating trust-region method are presented.