| 基于修正拟牛顿方程的两阶段非单调稀疏对角变尺度梯度投影算法 |
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| 引用本文： | 宫恩龙,段立宁,高苗苗,王真真,朱明月,孙清滢,杜小雨.基于修正拟牛顿方程的两阶段非单调稀疏对角变尺度梯度投影算法[J].数学的实践与认识,2017(6):233-242. |
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| 作者姓名： | 宫恩龙 段立宁 高苗苗 王真真 朱明月 孙清滢 杜小雨 |
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| 作者单位： | 1. 青岛酒店管理职业技术学院,山东青岛,266100;2. 中国石油大学(华东)理学院,山东青岛,266580 |
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| 基金项目： | 国家自然科学基金(61201455)，中央高校基本科研业务费专项资金(10CX04044A |
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| 摘 要： | 基于修正拟牛顿方程,利用Goldstein-Levitin-Polyak(GLP)投影技术,建立了求解带凸集约束的优化问题的两阶段步长非单调变尺度梯度投影算法,证明了算法的全局收敛性和一定条件下的Q超线性收敛速率.数值结果表明新算法是有效的,适合求解大规模问题.
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| 关 键 词： | 修正拟牛顿方程 Goldstein-Levitin-Polyak(GLP)投影 非单调线搜索 收敛 超线性收敛速率 |
Nonmonotone Two Stages Diagonal Sparse Variable Metric Gradient Projection Method Based on Modified Quasi-Newton Equation |
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| GONG En-long,DUAN Li-ning,GAO Miao-miao,WANG Zhen-zhen,ZHU Ming-yue,SUN Qing-ying,DU Xiao-yu.Nonmonotone Two Stages Diagonal Sparse Variable Metric Gradient Projection Method Based on Modified Quasi-Newton Equation[J].Mathematics in Practice and Theory,2017(6):233-242. |
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| Authors: | GONG En-long DUAN Li-ning GAO Miao-miao WANG Zhen-zhen ZHU Ming-yue SUN Qing-ying DU Xiao-yu |
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| Abstract: | Based on modified quasi-Newton equation,by combining with Goldstein-LevitinPolyak(GLP) projection technique,a new non monotone two stages stepsize variable metric gradient projection method for convex set constrained optimization problem is presented.The global convergence property of the algorithm is proved.Under some reasonable conditions,it is proved that the algorithm has Q-superlinear convergence rate.The numerical results show that the new method is effective and is fit to solve large-scale problems. |
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| Keywords: | modified quasi-Newton equation Goldstein-Levitin-Polyak(GLP) projection non-monotone line search convergence superlinear convergence rate |
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