LUO Wenjun,WU Zezhong,HE Shengyu.An Improved Quasi-Newtonian Algorithm[J].Journal of Chengdu University of Information Technology,2024,39(03):374-381.[doi:10.16836/j.cnki.jcuit.2024.03.016]
一类改进的拟牛顿算法
- Title:
- An Improved Quasi-Newtonian Algorithm
- 文章编号:
- 2096-1618(2024)03-0374-08
- Keywords:
- DFP; conjugate gradient; quasi-Newtonian method; unconstrained optimization; linear search
- 分类号:
- O221.2
- 文献标志码:
- A
- 摘要:
- 在拟牛顿方程基础上,推导出一种新的DFP校正公式,并在强Wolfe步长规则下给出一类新的DFP算法。随后提出一种改进的强Wolfe线性搜索法,改善由于精度所导致的线性搜索失败的问题,并在一定假设下证明改进的算法具有全局收敛性。最后用算例来改进前后的DFP算法的性能作对比,结果表明改进的算法行之有效,并且具有更好的收敛性。
- Abstract:
- In this paper, based on the new quasi-Newtonian equation, a new DFP correction formula is derived, and a new class of DFP algorithm is proposed under the strong Wolfe condition. Then, we propose an improved strong Wolfe linear search method to solve the problem of linesearch failure due to accuracy, and prove that the improved algorithm has global convergence under certain assumptions. Finally, an example is introduced to compare the performance of the DFP algorithm before and after the improvement. The results show that the improved algorithm is moreeffective and has better convergence.
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备注/Memo
收稿日期:2022-11-29
基金项目:国家自然科学基金资助项目(71962030); 四川省社科重点研究基地资助项目(Xq21B06); 国家社会科学基金资助项目(21BTQ099)