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This paper describes and establishes the iteration-complexity of a doublyaccelerated inexact proximal point (D-AIPP) method for solving the nonconvexcomposite minimization problem whose objective function is of the form $f+h$where $f$ is a (possibly nonconvex) differentiable function whose gradient isLipschitz continuous and $h$ is a closed convex function with bounded domain.D-AIPP performs two types of iterations, namely, inner and outer ones. Itsouter iterations correspond to the ones of the accelerated inexact proximalpoint scheme. Its inner iterations are the ones performed by an acceleratedcomposite gradient method for inexactly solving the convex proximal subproblemsgenerated during the outer iterations. Thus, D-AIPP employs both inner andouter accelerations.

A Doubly Accelerated Inexact Proximal Point Method for Nonconvex Composite Optimization Problems