this talk introduces a unified proximal gradient method with extrapolation (upg-e) to solve a class of nonconvex and nonsmooth composite optimization. upg-e provides unified treatment to both convex and nonconvex problems, and adaptively estimates the nonconvexity modulus of the possibly nonconvex component function in the objective function. in this talk, we will discuss the global convergence and convergence rate of upg-e for solving both convex and nonconvex composite optimization. we will also show the promising numerical performance of upg-e compared with other well-established proximal gradient methods in the literature.