# A family of multi-parameterized proximal point algorithms

## TL;DR

This paper introduces a new multi-parameterized proximal point algorithm with relaxation for convex optimization with linear constraints, demonstrating improved convergence and performance over existing methods.

## Contribution

The paper develops a novel multi-parameterized proximal point algorithm with relaxation, providing convergence analysis and empirical evidence of superior performance.

## Key findings

- Proven global convergence of the algorithm.
- Achieved sublinear convergence rate.
- Numerical experiments show better performance than existing methods.

## Abstract

In this paper, a multi-parameterized proximal point algorithm combining with a relaxation step is developed for solving convex minimization problem subject to linear constraints. We show its global convergence and sublinear convergence rate from the prospective of variational inequality. Preliminary numerical experiments on testing a sparse minimization problem from signal processing indicate that the proposed algorithm performs better than some well-established methods