A linearly convergent method for solving high-order proximal operator

TL;DR

This paper introduces a new linearly convergent algorithm for efficiently solving high-order proximal operators in convex optimization, improving computational performance over existing methods.

Contribution

The paper proposes a novel linearly convergent method for high-order proximal operators, extending classical proximal techniques with improved convergence guarantees.

Findings

The method demonstrates linear convergence in solving high-order proximal operators.

Experimental results show enhanced efficiency compared to previous approaches.

The approach is applicable to a broad class of convex optimization problems.

Abstract

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.