一种基于模拟退火思想的锥模型信赖域方法  

A Conic Model Trust Region Method Based on Idea of Simulated Annealing

作　　者：杨月婷[1] 王宏博 周国玲 李蓉 曹名圆[1] YANG Yueting;WANG Hongbo;ZHOU Guoling;LI Rong;CAO Mingyuan(School of Mathematics and Statistics,Beihua University,Jilin 132013,China)

机构地区：[1]北华大学数学与统计学院,吉林吉林132013

出　　处：《北华大学学报（自然科学版）》2022年第6期701-707,共7页Journal of Beihua University（Natural Science）

基　　金：吉林省自然科学基金联合基金重点项目(YDZJ202101ZYTS167,YDZJ202101ZYTS156,YDZJ202201ZYTS303);吉林省科技发展计划项目(20190303132SF);吉林省教育厅科学技术研究项目(JJKH20210030KJ).

摘　　要：针对无约束优化问题,提出一种基于简化锥模型的信赖域方法.该方法将模拟退火思想改进的Metropolis准则和简化锥模型信赖域方法相结合,即用标量矩阵近似Hessian矩阵,再由Metropolis准则接受更多的试探步.在适当的条件下,建立了新算法的全局收敛性.数值结果表明,该方法是有效的.A trust region method based on simple conic model is proposed for unconstrained optimization prob-lems.The Metropolis criterion improved by idea of simulated annealing is combined with the simple conic model trust region method,namely,Hessian matrix is approximated by a scalar matrix,and the Metropolis criterion is used to accept more trial steps.Under appropriate conditions,the global convergence of algorithm is established.Numerical results show that the new method is effective.

关 键 词：模拟退火思想 METROPOLIS准则 信赖域方法 全局收敛性 

分 类 号：O224.2[理学—运筹学与控制论]