Complexity of Inexact Proximal Newton methods

Recently several, so-called, proximal Newton methods were proposed for sparse optimization [6, 11, 8, 3]. These methods construct a composite quadratic approximation using Hessian information, optimize this approximation using a first-order method, such as coordinate descent and employ a line search to ensure sufficient descent. Here we propose a general framework, which includes slightly modified versions of existing algorithms and also a new algorithm, and provide a global convergence rate analysis in the spirit of proximal gradient methods, which includes analysis of method based on coordinate descent.