A preconditioned difference of convex functions algorithm with extrapolation and line search

TL;DR

This paper introduces an advanced proximal difference-of-convex algorithm with extrapolation and line search, improving convergence and efficiency for non-convex optimization problems, validated on classification and image segmentation tasks.

Contribution

It presents a novel DC algorithm with adaptive extrapolation and line search, ensuring global convergence and enhanced performance over existing methods.

Findings

Demonstrates faster convergence compared to existing DC algorithms.

Achieves higher solution accuracy in non-convex problems.

Validates effectiveness on classification and image segmentation tasks.

Abstract

This paper proposes a novel proximal difference-of-convex (DC) algorithm enhanced with extrapolation and aggressive non-monotone line search for solving non-convex optimization problems. We introduce an adaptive conservative update strategy of the extrapolation parameter determined by a computationally efficient non-monotone line search. The core of our algorithm is to unite the update of the extrapolation parameter with the step size of the non-monotone line search interactively. The global convergence of the two proposed algorithms is established through the Kurdyka-{\L}ojasiewicz properties, ensuring convergence within a preconditioned framework for linear equations. Numerical experiments on two general non-convex problems: SCAD-penalized binary classification and graph-based Ginzburg-Landau image segmentation models, demonstrate the proposed method's high efficiency compared to existing DC algorithms both in convergence rate and solution accuracy.