A family of spectral gradient methods for optimization
A family of spectral gradient methods for optimization
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一系列用于优化的光谱梯度方法
DOI：
10.1007/s10589-019-00107-8
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发表时间：
2019
影响因子：
2.2
通讯作者：
Liu Xin Wei
中科院分区：
文献类型：
--
作者：
Dai Yu Hong;Huang Yakui;Liu Xin Wei
我们提出了一组谱梯度方法，其步长由长Barzilai-Borwein （BB）步长和短BB步长的凸组合决定。在最小二乘的意义上，证明了这个族的每一个成员都具有某些准牛顿性质。该家族还包括一些其他的梯度方法作为其特殊情况。证明了二维严格凸二次方程的一类方法是超线性收敛的。此外，族在任何维情况下都是r -线性收敛的。给出了不同设置下的家庭数值结果，证明了该家庭是有希望的。
We propose a family of spectral gradient methods, whose stepsize is determined by a convex combination of the long Barzilai–Borwein (BB) stepsize and the short BB stepsize. Each member of the family is shown to share certain quasi-Newton property in the sense of least squares. The family also includes some other gradient methods as its special cases. We prove that the family of methods isR-superlinearly convergent for two-dimensional strictly convex quadratics. Moreover, the family isR-linearly convergent in the any-dimensional case. Numerical results of the family with different settings are presented, which demonstrate that the proposed family is promising.