A linearly convergent method for solving high-order proximal operator

Recently, various high-order methods have been developed to solve the convex optimization problem. The auxiliary problem of these methods shares the general form that is the same as the high-order proximal operator proposed by Nesterov. In this paper, we present a linearly convergent method to solve the high-order proximal operator based on the classical proximal operator. In addition, some experiments are performed to demonstrate the performance of the proposed method.