Nesterov加速拟牛顿法研究及其化工应用  

Nesterov Accelerated Quasi-Newton Method Research and Chemical Applications

作　　者：吕佳泽 赵军[1] 陶少辉[1] 陈玉石[2] 孙晓岩[1] 项曙光[1] LYU Jiaze;ZHAO Jun;TAO Shaohui;CHEN Yushi;SUN Xiaoyan;XIANG Shuguang(Institute of Process Systems Engineering,Qingdao University of Science and Technology,Qingdao 266042,China;Petro-Cyber Works Information Technology Co.,Ltd.,Shanghai 200040,China)

机构地区：[1]青岛科技大学过程系统工程研究所,山东青岛266042 [2]石化盈科信息技术有限责任公司,上海200400

出　　处：《青岛科技大学学报(自然科学版)》2025年第1期60-66,共7页Journal of Qingdao University of Science and Technology:Natural Science Edition

基　　金：国家自然科学基金项目(22178190).

摘　　要：拟牛顿法是化工过程模拟中一种常用的非线性方程组求解算法,提高其收敛性和计算效率对于流程模拟软件开发有着重要意义。本工作基于Nesterov加速拟牛顿法,给出其使用4种更新方法的改进形式。通过求解经典低维非线性方程组问题和典型化工流程设计规定问题,比较了Nesterov加速4种拟牛顿法的计算效率。计算结果表明:基于CGBM更新方法的加速拟牛顿法在所测试的15组问题中计算成功率为93.3%,计算效率最高;而BFGS更新方法在化工设计规定问题中对于Jacobi矩阵的近似效果较差,计算成功率为60%,计算性能最低。Nesterov加速拟牛顿法已被成功应用于国产化工流程模拟软件,对于工业软件的国产化具有重要意义。Quasi-Newton method is a general algorithm for solving nonlinear equations in chemical process simulation.Improving its convergence and computational efficiency is of great significance for the development of process simulation software.Based on Nesterov accelerated quasi-Newton method,this paper gives four kinds of modified forms of using different updating formula.By solving the classic low-dimensional nonlinear equations problem and typical chemi-cal process design specs,compared the Nesterov accelerated quasi-Newton method and four kinds of the modified algorithm has better computation efficiency.The calculation results show that the accelerated quasi Newton method based on CGBM updating method has the highest calculation efficiency with a success rate of 93.3%in 15 groups of problems tested.However,the BFGS updating method has a poor approximation effect on Jacobi matrix in the chemical engineering design regulations,with a calculation success rate of 60%and the lowest calcula-tion performance.Nesterov accelerated quasi-Newton method has been successfully applied to domestic chemical process simulation software,which is of great significance for the localiza-tion of industrial software.

关 键 词：非线性方程组 拟牛顿法 Nesterov加速 化工流程模拟 

分 类 号：TQ015.9[化学工程] TP391.9[自动化与计算机技术—计算机应用技术]