# A parameterized proximal point algorithm for separable convex optimization

## TL;DR

This paper introduces a parameterized proximal point algorithm designed for separable convex optimization problems, demonstrating global convergence and superior performance over existing methods in numerical experiments.

## Contribution

The paper proposes a novel parameterized proximal point algorithm with proven convergence and improved efficiency for solving separable convex programming problems.

## Key findings

- Global convergence with O(1/t) rate established
- Numerical results show better performance than ADMM and relaxed PPA
- Effective for sparse optimization in statistical learning

## Abstract

In this paper, we develop a parameterized proximal point algorithm (P-PPA) for solving a class of separable convex programming problems subject to linear and convex constraints. The proposed algorithm is provable to be globally convergent with a worst-case O(1/t) convergence rate, wheret denotes the iteration number. By properly choosing the algorithm parameters, numerical experiments on solving a sparse optimization problem arising from statistical learning show that our P-PPA could perform significantly better than other state-of-the-art methods, such as the alternating direction method of multipliers and the relaxed proximal point algorithm.