We study a nonmonotone adaptive Barzilai-Borwein gradient algorithm for -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 -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.
Yuanying Qiu. Jianlei Yan. Fanyong Xu. "Nonmonotone Adaptive Barzilai-Borwein Gradient Algorithm for Compressed Sensing." Abstr. Appl. Anal. 2014 (SI43) 1 - 6, 2014. https://doi.org/10.1155/2014/410104