A Diagonal BFGS Update Algorithm with Inertia Acceleration Technology for Minimizations

TL;DR

This paper introduces a novel diagonal BFGS update algorithm enhanced with inertia acceleration for non-convex constrained minimization, demonstrating improved convergence and promising empirical results.

Contribution

It combines diagonal quasi-Newton updates with inertia acceleration and extrapolation techniques, specifically targeting non-convex constrained problems for better convergence.

Findings

Achieves global linear convergence under certain conditions

Demonstrates superior data results in experiments

Effectively handles non-convex constrained optimization

Abstract

We integrate the diagonal quasi-Newton update approach with the enhanced BFGS formula proposed by Wei, Z., Yu, G., Yuan, G., Lian, Z. \cite{b1}, incorporating extrapolation techniques and inertia acceleration technology. This method, designed specifically for non-convex constrained problems, requires that the search direction ensures sufficient descent and establishes global linear convergence. Such a design has yielded exceptionally favorable data results.