A fast conjugate gradient algorithm with active set prediction for l1 optimization

In this paper, we develop an active set identification technique for solving optimization problems. Such a technique has a strong ability to accurately identify the zero components in a neighbourhood of an optimal solution. Based on the active set identification technique, we propose a conjugate gradient algorithm for solving optimization problems. Under appropriate conditions, we show that the method is globally convergent. To accelerate the algorithm, a subspace exact steplength and a preconditioned strategy are proposed and integrated with the algorithm to solve the well-known problems. Numerical experiments with compressive sensing problems show that our approach is competitive with several known methods.