Conjugate Gradient Methods And Nesterov-type Methods For Solving Lasso Problem

Signal and image restoration problems are often related to finding the sparsest so-lution of large-scale and under-determined linear system. An approximation to under-determined linear systems is usually called Lasso problem. This problem is a convex minimization problem. The forward-backward splitting operator method is important for solving it. Accelerated version was proposed to improve the method’s convergence rate. In this thesis, we prove the convergence rate of an inexact accelerated forward-backward splitting method proposed by Salzo[20] and show its effectiveness by preliminary exper-iment. We consider a variant of Lasso problem. Its objective function is differentiable. This problem can be solved by nonlinear conjugate gradient method. We show the effec-tiveness of PR+method proposed by Dong[4] and RMPRP method proposed by Li[14] by preliminary experiment.