Inexact Proximal-gradient Algorithms For Composite Convex Optimization Problem And Their Applications

Composite convex optimization problem is one of the important optimization problems.It has a wide range of applications in the sparse signal restoration,sparse image regression,sparse inverse variance,sparse dictionary learning,image restoration,image denoising and deblurring and so on.This article mainly studies the following:Firstly,based on the idea of proximal-gradient algorithm and ?-subdifferential,we propose an inexact proximal-gradient algorithm with backtracking technique for composite convex optimization by considering the errors in the calculation of the gradient of the smooth term and in the proximity operator,and analyse the convergence rate analysis of the algorithm under mild conditions.Moreover,we apply it to solve the Lasso problem and sparse logistic regression problem.Secondly,based on restart technique,we propose an inexact proximal-gradient algorithm with restart and backtracking techniques for composite convex optimization.The convergence rate analysis of the algorithm is given under mild conditions,we also discuss its application in Lasso problem and sparse logistic regression problem.For the above two algorithms,the corresponding numerical experiments show their effectivenesses.