| 基于三阶拟牛顿方程的对角三阶拟牛顿法 |
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| 引用本文： | 冯茹茹,王希云.基于三阶拟牛顿方程的对角三阶拟牛顿法[J].太原重型机械学院学报,2012(1):58-61. |
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| 作者姓名： | 冯茹茹 王希云 |
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| 作者单位： | 太原科技大学应用科学学院,太原030024 |
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| 基金项目： | 山西省自然科学基金（2008011013） |
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| 摘 要： | 基于三阶拟牛顿方程,结合Zhang H.C.提出的非单调线搜索规则设计了求解大规模无约束优化问题的对角三阶拟牛顿算法。该算法在每次迭代中利用对角矩阵逼近Hessen矩阵的逆,使存储量和计算量明显减少,并且证明了算法的全局收敛性和超线性收敛性。数值试验表明该算法是有效的。
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| 关 键 词： | 无约束优化 三阶拟牛顿方程 非单调线搜索 收敛性 |
A Diagonal Three-order Quasi-Newton Method Based on Three-order Quasi-Newton Equation |
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| FENG Ru-ru,WANG Xi-yun.A Diagonal Three-order Quasi-Newton Method Based on Three-order Quasi-Newton Equation[J].Journal of Taiyuan Heavy Machinery Institute,2012(1):58-61. |
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| Authors: | FENG Ru-ru WANG Xi-yun |
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| Affiliation: | (School of Applied Sciences,Taiyuan University of Science and Technology,Taiyuan 030024,China) |
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| Abstract: | In this paper,we propose a diagonal three-order quasi-Newton method for large-scale unconstrained optimization problems,which is based on three-order quasi-Newton equation and Zhang H.C.non-monotone line search rule.The inverse of Hessen approximation in diagonal matrix form can be obtained,thus avoiding the computational and storing expenses of iterations.The global convergence of the new method is achieved,and the superlinear convergence property is further analyzed.Numerical results show that this method is efficient. |
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| Keywords: | unconstrained optimization tree-order quasi-Newton equation non-montonic linear search convergence |
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