# Accelerated method of finding for the minimum of arbitrary Lipschitz convex function

## TL;DR

This paper introduces a novel optimization method for nonsmooth convex functions that achieves superlinear convergence by using a variable-dependent averaging technique, enabling second-order methods on smooth approximations.

## Contribution

It develops a new approximation approach using set-valued mappings that transforms nonsmooth convex functions into twice differentiable convex functions for faster optimization.

## Key findings

- Achieves superlinear convergence rate.
- Transforms nonsmooth functions into smooth approximations.
- Enables second-order optimization methods on nonsmooth problems.

## Abstract

The goal of the paper is development of an optimization method with the superlinear convergence rate for a nonsmooth convex function. For optimization an approximation is used that is similar to the Steklov integral averaging. The difference is that averaging is performed over a variable-dependent set, that is called a set-valued mapping (SVM) satisfying simple conditions. Novelty approach is that with such an approximation we obtain twice continuously differentiable convex functions, for optimizations of which are applied methods of the second order. The estimation of the convergence rate of the method is given.