| 一类修正正割方法解非线性约束优化问题的超线性收敛性 |
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| 引用本文： | 王祝君,朱德通.一类修正正割方法解非线性约束优化问题的超线性收敛性[J].上海师范大学学报(自然科学版),2008,37(5):459-467. |
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| 作者姓名： | 王祝君 朱德通 |
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| 作者单位： | 1. 上海师范大学,数理信息学院,上海,200234
2. 上海师范大学,商学院,上海,200234 |
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| 基金项目： | 高等学校博士学科点专项科研项目，上海市重点学科建设项目，上海市教育厅科学基金 |
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| 摘 要： | 提出了一类解非线性等式约束优化问题的修正正割方法.通过应用二阶校正技术改进搜索方向,修正由Fotecilla提出的产生二步超线性收敛的正割方法.证明了在合理的假设条件下该算法具有一步超线性收敛性.数据结果表明了本算法的有效性.
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| 关 键 词： | 约束优化 正割算法 二阶校正 |
Superlinear convergence of improved secant methods for nonlinear constrained optimization |
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| WANG Zhu-jun,ZHU De-tong.Superlinear convergence of improved secant methods for nonlinear constrained optimization[J].Journal of Shanghai Normal University(Natural Sciences),2008,37(5):459-467. |
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| Authors: | WANG Zhu-jun ZHU De-tong |
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| Institution: | WANG Zhu-jun, ZHU De-tong(1. College of Mathematics and Sciences, Shanghai Normal University, Shanghai 200234, China ; 2. College of Business, Shanghai Normal University, Shanghai 200234, China) |
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| Abstract: | We propose a class of improved secant methods for nonlinear equality constrained optimization based on adding second order correction steps. The new methods differ from the original secant methods introduced by Fontecilla that generate a sequence converging two-step q-superlinearly. Under mild assumptions it is shown that the new algorithms can improve the search direction so that the local one-step superlinear convergence is achieved. The numerical results indicate that the improved algorithms are effective. |
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| Keywords: | constrained optimization secant algorithm second order correction |
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