An interacting particle consensus method for constrained global optimization

TL;DR

This paper introduces a particle-based optimization method for constrained minimization problems, combining consensus algorithms with a forcing term, and provides theoretical convergence analysis and numerical validation.

Contribution

The paper develops a novel particle method for constrained optimization, integrating a forcing term and establishing mean-field convergence with a stable discretized algorithm.

Findings

Proven convergence of the mean-field limit to the constrained minimizer.

Development of a stable discretized algorithm for practical implementation.

Numerical experiments demonstrating the method's effectiveness.

Abstract

This paper presents a particle-based optimization method designed for addressing minimization problems with equality constraints, particularly in cases where the loss function exhibits non-differentiability or non-convexity. The proposed method combines components from consensus-based optimization algorithm with a newly introduced forcing term directed at the constraint set. A rigorous mean-field limit of the particle system is derived, and the convergence of the mean-field limit to the constrained minimizer is established. Additionally, we introduce a stable discretized algorithm and conduct various numerical experiments to demonstrate the performance of the proposed method.