摘要
高效率求解无约束二次凸优化问题是优化算法设计的重要任务.针对这类问题,本文提出了一种修正的Cauchy-Barzilai-Borwein算法,简称为MCBB算法.文章证明了MCBB算法对于无约束二次严格凸优化问题具有全局收敛和Q-线性收敛速率.初步的数值对比实验表明,对于坏条件问题,MCBB算法比CBB与BB算法更为有效.
Efficient-solver of unconstrained quadratic convex optimization problem is an important component of optimization algorithms. This paper proposes a modified Cauchy-Barzilai- Borwein method for unconstrained quadratic and strongly convex optimization problem. The proposed method is abbreviated to MCBB. The global convergence and Q-linear con- vergence rate of MCBB method are proved. Elementary numerical tests show that, compared with CBB and BB methods, MCBB method is more effective, especially for ill-conditioned problems.
出处
《数值计算与计算机应用》
CSCD
2016年第3期186-198,共13页
Journal on Numerical Methods and Computer Applications
基金
国家自然科学基金(11571074)
福建省自然科学基金(2015J01010)
福建省教育厅科技计划重点项目(JA14037)
关键词
CBB算法
MCBB算法
二次严格凸优化
全局收敛
线性收敛
CBB method
MCBB method
quadratic and strongly convex optimiza-tion
global convergence
Q-linear convergence rate.
