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A family of spectral gradient methods for optimization

Yu-Hong Dai (dyh***at***lsec.cc.ac.cn)
Yakui Huang (huangyakui2006***at***gmail.com)
Xin-Wei Liu (optim2008***at***163.com)

Abstract: We propose a family of spectral gradient methods, whose stepsize is determined by a convex combination of the short Barzilai-Borwein (BB) stepsize and the long BB stepsize. It is shown that each member of the family shares 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 is $R$-superlinearly convergent for two-dimensional strictly convex quadratics. Moreover, the family is $R$-linearly convergent in the $n$-dimensional case. Numerical results of the family with different settings are presented, which demonstrate that the proposed family is promising.

Keywords: unconstrained optimization; steepest descent method; spectral gradient method; $R$-linear convergence; $R$-superlinear convergence

Category 1: Convex and Nonsmooth Optimization (Convex Optimization )

Category 2: Nonlinear Optimization (Unconstrained Optimization )


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Entry Submitted: 05/18/2018
Entry Accepted: 05/18/2018
Entry Last Modified: 12/07/2018

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