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| A Derivative-Free Optimization Algorithm Combining Line-Search and Trust-Region Techniques* |
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Citation： |
Pengcheng XIE,Ya-xiang YUAN.A Derivative-Free Optimization Algorithm Combining Line-Search and Trust-Region Techniques*[J].Chinese Annals of Mathematics B,2023,44(5):719~734 |
| Page view： 1036
Net amount： 630 |
Authors： |
Pengcheng XIE; Ya-xiang YUAN |
Foundation： |
National Natural Science Foundation of China (No. 12288201). |
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| Abstract： |
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. |
Keywords： |
Nonlinear optimization, Derivative-Free, Quadratic model, Line-Search,Trust-Region |
Classification： |
90C56, 90C30, 65K05, 90C90 |
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