摘要
对无约束优化问题提出了对角稀疏拟牛顿法,该算法采用了
Armijo非精确线性搜索,并在每次迭代中利用对角矩阵近似拟牛顿法中的校正矩阵,使计算搜索
方向的存贮量和工作量明显减少,为大型无约束优化问题的求解提供了新的思路. 在通常的
假设条件下,证明了算法的全局收敛性,线性收敛速度并分析了超线性收敛特征。数值实验表明算
法比共轭梯度法有效,适于求解大型无约束优化问题.
Abstract
In this paper, we present a diagonal-sparse quasi-Newton method for
unconstrained optimization problems. The method is similar to
quasi-Newton method, but restricts the quasi-Newton matrix to a sparse matrix, and uses
approximate quasi-Newton condition to determine a search direction and uses Armijo's
line search rule to define a step-size at each iteration.
It avoids the storage and computation of
some matrices in its iteration, so that it is suitable for solving large scale optimization problems.
Under some mild assumptions, we prove
the global convergence and linear convergence
rate, and futher analyze the superlinear convergence property of this method.
Numerical experiments show that the diagonal-sparse
quasi-Newton method is suitable to solve large scale problems, especially the problems
in which the Hesse matrix of objective functions is sparse. Numerical results also show that
the new method is more efficient than other similar methods, such as Cauchy method, conjugate
gradient method, etc.
关键词
对角稀疏拟牛顿法 /
非精确搜索 /
全局收敛性 /
收敛速度.
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Key words
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时贞军
, 孙国.
, {{custom_author.name_cn}}.
无约束优化问题的对角稀疏拟牛顿法. 系统科学与数学, 2006, 26(1): 101-112. https://doi.org/10.12341/jssms08720
Shi Zhenjun
, Sun Guo.
, {{custom_author.name_en}}.
A Diagonal-Sparse Quasi-Newton Method for Unconstrained Optimization Problem. Journal of Systems Science and Mathematical Sciences, 2006, 26(1): 101-112 https://doi.org/10.12341/jssms08720
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脚注
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