| 一个锥模型的自适应信赖域算法及其收敛性 |
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| 引用本文： | 冯琳,段复建. 一个锥模型的自适应信赖域算法及其收敛性[J]. 数学杂志, 2016, 36(1): 144-156 |
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| 作者姓名： | 冯琳 段复建 |
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| 作者单位： | 重庆文理学院数学与财经学院, 重庆 402160,桂林电子科技大学数学与计算科学学院, 广西 桂林 541004 |
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| 基金项目： | 国家自然科学基金(11061011);广西自然科学基金(2011GXNSFA018138);重庆文理学院课题(Y2013sc42). |
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| 摘 要： | 本文研究了无约束最优化问题的基于锥模型的自适应信赖域算法.利用理论分析得到一个新的自适应信赖域半径.算法在每步迭代中以变化的速率、当前迭代点的信息以及水平向量信息调节信赖域半径的大小.从理论上证明了新算法的全局收敛性和Q-二阶收敛性.用数值试验验证了新算法的有效性.推广了已有的自适应信赖域算法的可行性和有效性.
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| 关 键 词： | 无约束最优化 信赖域方法 锥模型 自适应 收敛性 |
| 收稿时间： | 2011-10-13 |
| 修稿时间： | 2012-03-01 |
A SELF-ADAPIVE TRUST REGION METHOD AND ITS CONVERGENCE WITH THE CONIC MODEL |
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| FENG Lin and DUAN Fu-jian. A SELF-ADAPIVE TRUST REGION METHOD AND ITS CONVERGENCE WITH THE CONIC MODEL[J]. Journal of Mathematics, 2016, 36(1): 144-156 |
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| Authors: | FENG Lin and DUAN Fu-jian |
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| Affiliation: | School of Math. and Finance, Chongqing University of Arts and Sciences, Chongqing 402160, China and School of Math. and Comput. Sci., Guilin University of Electronic Technology, Guilin 541004, China |
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| Abstract: | In this paper, we study a self-adaptive trust region algorithm based on the conic model for unconstrained optimization problems. A new self-adaptive trust region radius is produced under theoretical analysis. At each iterative, the trust region radius is updated at a variable rate, the information at the current point and the level vector information. We analyze the global convergence and Q-quadratic convergence of the new method. Numerical results are also presented to test the efficiency of the new method which extend the application and efficiency of self-adaptive trust region algorithms. |
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| Keywords: | unconstrained optimization trust region method conic model self-adaptive convergence |
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