calmness/metric subregularity for set-valued maps is a powerful stability concept in variational analysis. in this talk we first discuss the concept of calmness/metric subregularity and sufficient conditions for verifying it. then we introduce a perturbation technique for conducting linear convergence analysis of various first-order algorithms for a class of nonsmooth optimization problems which minimizes the sum of a smooth function and a nonsmooth function by using the proximal gradient method as an example. this new perturbation technique enables us to provide some concrete sufficient conditions for checking linear convergence for very general problems where the nonconvexity may appear in each component of the objective function and leads to some improvement for the linear convergence results even for the convex case.