| 非线性等式与有界约束优化问题的正割算法 |
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| 引用本文： | 顾 超,朱德通.非线性等式与有界约束优化问题的正割算法[J].数学年刊A辑(中文版),2016,37(2):191-210. |
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| 作者姓名： | 顾 超 朱德通 |
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| 作者单位： | 上海立信会计学院数学与信息学院, 上海 201620. E-mail: guchao@lixin.edu.cn,上海师范大学数学系, 上海 200234. E-mail: dtzhu@shnu.edu.cn |
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| 基金项目： | 本文受到国家自然科学基金 (No.11201304, No.11371253)和上海市教育委员会科研创新项目的资助. |
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| 摘 要： | 提出了结合仿射尺度技术的正割算法解非线性等式与有界约束优化问题.
在合理假设下, 证明了渐弱滤子线搜索方法可以保证新算法具有整体收敛性.
通过引入一个高阶修正方向, 克服Maratos效应的影响, 使得算法二步$q$-\!\!超线性收敛于最优点.
进一步地, 对算法进行修改, 使得新算法达到$q$-\!\!超线性收敛性.
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| 关 键 词： | 正割算法 仿射尺度技术 线搜索 渐弱滤子方法 收敛性 |
| 收稿时间： | 2014/2/19 0:00:00 |
| 修稿时间： | 2015/9/15 0:00:00 |
Convergence of the Secant Algorithm for Nonlinear Equality and Box-Constrained Optimization |
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| GU Chao and ZHU Detong.Convergence of the Secant Algorithm for Nonlinear Equality and Box-Constrained Optimization[J].Chinese Annals of Mathematics,2016,37(2):191-210. |
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| Authors: | GU Chao and ZHU Detong |
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| Institution: | School of Mathematics and Information Science, Shanghai Lixin University of Commerce, Shanghai 201620, China. E-mail: guchao@lixin.edu.cn and Department of Mathematics, Shanghai Normal University, Shanghai 200234, China. E-mail: dtzhu@shnu.edu.cn |
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| Abstract: | The authors propose a new secant algorithm with the affine scaling technique for nonlinear equality and box-constrained optimization.
The new algorithm with the line search dwindling filter method yields the global convergence under some reasonable conditions.
A high-order modified direction is introduced in order to prevent the Maratos effect so that the algorithm converges locally two-step $q$-superlinearly.
Furthermore, with some modifications, the convergence rate of the new approach is $q$-superlinear. |
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| Keywords: | Secant algorithm Affine scaling technique Line search Dwindling filter method Convergence |
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