| 局部误差的有界约束非线性方程组的非单调信赖域算法 |
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| 引用本文： | 贾春霞,朱德通.局部误差的有界约束非线性方程组的非单调信赖域算法[J].运筹学学报,2008,12(2):25-40. |
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| 作者姓名： | 贾春霞 朱德通 |
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| 作者单位： | 上海师范大学数理信息学院,上海,200234 |
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| 基金项目： | 国家自然科学基金
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the Ph. D. Foundation Grant
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the Shanghai Leading Academic Discipline Project
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The Science Foundation |
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| 摘 要： | 本文提供了在没有非奇异假设的条件下,求解有界约束半光滑方程组的投影信赖域算法.基于一个正则化子问题,求得类牛顿步,进而求得投影牛顿步.在合理的假设条件下,证明了算法不仅具有整体收敛性而且保持超线性收敛速率.
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| 关 键 词： | 运筹学 信赖域 类牛顿步 投影牛顿步 局部超线性收敛 非线性系统 奇异 Operations research trust-region Newton-like step projected Newton step local superlinear convergence nonlinear systems singular 局部 误差 有界约束 线性方程组 非单调信赖域算法 Assumption Nonlinear Systems Method results numerical experiments show effectiveness nonmonotonic criterion progress contours function large curvature global convergence |
Nonmonotone Trust-Region Method for Solving Bound-constrained Nonlinear Systems without Nonsingular Assumption |
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| Jia Chunxia,Zhu Detong.Nonmonotone Trust-Region Method for Solving Bound-constrained Nonlinear Systems without Nonsingular Assumption[J].OR Transactions,2008,12(2):25-40. |
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| Authors: | Jia Chunxia Zhu Detong |
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| Abstract: | In this paper, we propose a projected trust-region algorithm for solving bound-constrained smooth systems of equations. Based on a regularized problem, we obtain the Newton-like step which generates the projected Newton step. The global convergence and fast local convergence rate of the proposed algorithm are established under some reasonable conditions without nonsingular assumption. A nonmonotonic criterion should bring about speeding up the convergence rate progress in the contours of the merit function with large curvature. Finally, the results of numerical experiments are reported to show the effectiveness of the proposed algorithm. |
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| Keywords: | Operations research trust-region Newton-like step projected Newton step local superlinear convergence nonlinear systems singular |
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