A Barzilai-Borwein type method for minimizing composite functions (Q494671)

In this paper, a Barzilai and Borwein type method [\textit{J. Barzilai} and \textit{J. M. Borwein}, IMA J. Numer. Anal. 8, No. 1, 141--148 (1988; Zbl 0638.65055)] is used to minimize the sum of a smooth function and a convex regularizer. The sublinear and R-linear convergence of the method is established when the objective function is convex and strongly convex, respectively. The efficiency of the method is illustrated by some numerical experimental results on \(l_2\)-\(l_1\) problems, image deblurring problems, group-separable regularizers, and total variation regularization problems.