A Derivative-Free Optimization Algorithm Combining Line-Search and Trust-Region Techniques  

作　　者：Pengcheng XIE Ya-xiang YUAN 

机构地区：[1]State Key Laboratory of Scientific/Engineering Computing,Institute of Computational Mathematicsand Scientific/Engineering Computing,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,University of Chinese Academy of Sciences,Beijing 100190,China

出　　处：《Chinese Annals of Mathematics,Series B》2023年第5期719-734,共16页数学年刊（B辑英文版）

基　　金：supported by the National Natural Science Foundation of China(No.12288201)。

摘　　要：The speeding-up and slowing-down(SUSD)direction is a novel direction,which is proved to converge to the gradient descent direction under some conditions.The authors propose the derivative-free optimization algorithm SUSD-TR,which combines the SUSD direction based on the covariance matrix of interpolation points and the solution of the trust-region subproblem of the interpolation model function at the current iteration step.They analyze the optimization dynamics and convergence of the algorithm SUSD-TR.Details of the trial step and structure step are given.Numerical results show their algorithm’s efficiency,and the comparison indicates that SUSD-TR greatly improves the method’s performance based on the method that only goes along the SUSD direction.Their algorithm is competitive with state-of-the-art mathematical derivative-free optimization algorithms.

关 键 词：Nonlinear optimization DERIVATIVE-FREE Quadratic model Line-Search TRUST-REGION 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程]