| 一类修正Hager-Zhang共轭梯度法的收敛性及其数值实验 |
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| 引用本文： | 王松华,夏师,黎勇.一类修正Hager-Zhang共轭梯度法的收敛性及其数值实验[J].吉林大学学报(理学版),2021,58(5):1107-1116. |
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| 作者姓名： | 王松华 夏师 黎勇 |
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| 作者单位： | 百色学院 数学与统计学院, 广西 百色533000 |
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| 摘 要： | 为有效提高求解无约束优化问题的计算效率, 提出一类新的修正Hager-Zhang共轭梯度法, 该算法不依赖线搜索, 具有充分下降性和信赖域性质. 理论研究结果表明, 在常规假设条件下, 新算法不仅在弱Wolfe-Powell线搜索下对一般函数全局收敛, 且对一致凸函数具有R-线性收敛速度. 数值实验结果表明, 新算法比经典Hager-Zhang算法及其两个修正算法性能更优.
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| 关 键 词： | 无约束优化 Hager-Zhang共轭梯度法 充分下降性 信赖域 收敛性 |
| 收稿时间： | 2019-12-05 |
A Non-monotonic SQCQP Algorithm for Semi-infinite Minimax Discretization Problems |
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| WANG Songhua,XIA Shi,LI Yong.A Non-monotonic SQCQP Algorithm for Semi-infinite Minimax Discretization Problems[J].Journal of Jilin University: Sci Ed,2021,58(5):1107-1116. |
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| Authors: | WANG Songhua XIA Shi LI Yong |
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| Institution: | School of Mathematics and Statistics, Baise University, Baise 533000, Guangxi Zhuang Autonomous Region, China |
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| Abstract: | Aiming at the problem of low computational efficiency of sequential quadratic programming (SQP) algorithms when dealing with semi-infinite minimax discretization problems with complex structures and large nonlinearities, we proposed a non-monotonic sequential quadratic constrained quadratic programming (SQCQP) algorithm, and proved the convergence of the algorithm under appropiate conditions. The results of numerical experiments show that the non-monotonic SQCQP algorithm is better than the SQP algorithm in reducing the number of iterations and calculation time when the discrete level is 100. |
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| Keywords: | minimax problem norm-relaxed strongly sub-feasible SQCQP algorithm non-monotonic technique |
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