王松华, 黎勇, 黄必昌.求解大规模非线性单调方程组的修正HS投影算法[J].河南理工大学学报（自然科学版）,2020,39(3):162-168.

WANG S H, LI Y, HUANG B C.A modified HS projection method for solving large scale nonlinearmonotone equations[J].Journal of Henan Polytechnic University(Natural Science) ,2020,39(3):162-168.

求解大规模非线性单调方程组的修正HS投影算法

王松华, 黎勇, 黄必昌

百色学院数学与统计学院，广西百色533000

摘要:为了更加高效求解大规模非线性单调方程组，克服其他算法存在的如算法复杂、编程难、储存量大等不足，在传统三项HS算法基础上，设计了一个新的搜索方向，并采用投影技术和新型线搜索构建了修正HS投影算法。该算法不依赖任何线搜索，具有充分下降性和信赖域性质，在一般假设条件下具有全局收敛性。初步数值试验表明，新算法的数值表现总体上比传统的HS算法和三项HS算法更优，鲁棒性更好，能够更加高效地求解大规模非线性单调方程组问题。

关键词:非线性方程组;共辄梯度法;充分下降性;信赖域性质;全局收敛性

doi:10.16186/j.cnki.1673-9787.2020.3.20

基金项目:国家自然科学基金资助项目（11661001， 11661009 ）；广西自然科学基金资助项目（2018GXNSFAA281259，

收稿日期:2019/07/17

修回日期:2019/08/22

出版日期:2020/05/15

A modified HS projection method for solving large scale nonlinearmonotone equations

WANG Songhua, LI Yong, HUANG Bichang

School of Mathematics and Statistics， Baise University，Baise 533000 ， Guangxi， China

Abstract:In order to overcome the shortcomings of other algorithms such as their complexity， programming difficulty and the large storage， and so on， and to solve efficiently large scale nonlinear monotone equations， a new search direction was put forward based on the traditional HS algorithm. Meanwhile， the HS projection method was modified by the projection technique and the search approach. The new algorithm had the sufficient descent property and trust region features without any line searches. Under some mild assumptions， the global convergence was proved. The numerical calculation results showed that the new algorithm was more excellent and had the better robustness comparing with traditional HS algorithm and Three tern HS algorithm. The new algorithm was more efficient for solving large scale nonlinear monotone equations.

Key words:nonlinear equations;conjugate gradient method;sufficient descent property;trust region trait;global convergence

求解大规模非线性单调方程组的修正HS投影算法_王松华.pdf