New Douglas-Rashford Splitting Algorithms for Generalized DC Programming with Applications in Machine Learning

TL;DR

This paper introduces new Douglas-Rashford splitting algorithms tailored for generalized DC programming, demonstrating improved convergence and efficiency in machine learning applications over existing methods.

Contribution

The paper develops novel Douglas-Rashford algorithms with enhanced convergence rates for nonconvex DC problems, validated through practical machine learning examples.

Findings

Algorithms outperform DCA and ADMM in efficiency

Convergence to critical points proven under reasonable conditions

Effective in solving real-world machine learning problems

Abstract

In this work, we propose some new Douglas-Rashford splitting algorithms for solving a class of generalized DC (difference of convex functions) in real Hilbert spaces. The proposed methods leverage the proximal properties of the nonsmooth component and a fasten control parameter which improves the convergence rate of the algorithms. We prove the convergence of these methods to the critical points of nonconvex optimization under reasonable conditions. We evaluate the performance and effectiveness of our methods through experimentation with three practical examples in machine learning. Our findings demonstrated that our methods offer efficiency in problem-solving and outperform state-of-the-art techniques like the DCA (DC Algorithm) and ADMM.