Nonmonotone Adaptive Barzilai-Borwein Gradient Algorithm for Compressed Sensing

Abstract

We study a nonmonotone adaptive Barzilai-Borwein gradient algorithm for $l_1$-norm minimization problems arising from compressed sensing. At each iteration, the generated search direction enjoys descent property and can be easily derived by minimizing a local approximal quadratic model and simultaneously taking the favorable structure of the $l_1$-norm. Under some suitable conditions, its global convergence result could be established. Numerical results illustrate that the proposed method is promising and competitive with the existing algorithms NBBL1 and TwIST.