Nonmonotone Adaptive Barzilai-Borwein Gradient Algorithm for Compressed Sensing

Abstract EN

We study a nonmonotone adaptive Barzilai-Borwein gradient algorithm for l1-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 l1-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.