Accelerated meta-algorithm for convex optimization problems

An envelope called an accelerated meta-algorithm is proposed. Based on the envelope, accelerated methods for solving convex unconstrained minimization problems in various formulations can be obtained from nonaccelerated versions in a unified manner. Quasi-optimal algorithms for minimizing smooth functions with Lipschitz continuous derivatives of arbitrary order and for solving smooth minimax problems are given as applications. The proposed envelope is more general than existing ones. Moreover, better convergence estimates can be obtained in the case of this envelope and better efficiency can be achieved in practice for a number of problem formulations.