A STOCHASTIC NEWTON METHOD FOR NONLINEAR EQUATIONS
作者机构：School of Mathematical SciencesDalian University of TechnologyDalianChina School of Mathematical SciencesUniversity of Chinese Academy of SciencesBeijingChina Peng Cheng LaboratoryShenzhenChina
出 版 物：《Journal of Computational Mathematics》 (计算数学（英文）)
年 卷 期：2023年第41卷第6期
页 面：1192-1221页
核心收录：
学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学]
基 金：supported by the National Natural Science Foundation of China (Nos.11731013,11871453 and 11971089) Young Elite Scientists Sponsorship Program by CAST (No.2018QNRC001) Youth Innovation Promotion Association,CAS Fundamental Research Funds for the Central Universities,UCAS
主 题：Nonlinear equations Stochastic approximation Line search Global convergence Computational complexity Local convergence rate
摘 要：In this paper,we study a stochastic Newton method for nonlinear equations,whose exact function information is difficult to obtain while only stochastic approximations are *** each iteration of the proposed algorithm,an inexact Newton step is first computed based on stochastic zeroth-and first-order *** encourage the possible reduction of the optimality error,we then take the unit step size if it is acceptable by an inexact Armijo line search ***,a small step size will be taken to help induce desired good *** we investigate convergence properties of the proposed algorithm and obtain the almost sure global convergence under certain *** also explore the computational complexities to find an approximate solution in terms of calls to stochastic zeroth-and first-order oracles,when the proposed algorithm returns a randomly chosen ***,we analyze the local convergence properties of the algorithm and establish the local convergence rate in high *** last we present preliminary numerical tests and the results demonstrate the promising performances of the proposed algorithm.
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