A Two-Phase Quasi-Newton Method for Optimization Problem

TL;DR

This paper introduces a novel two-phase quasi-Newton method for unconstrained optimization, demonstrating global convergence and superlinear local convergence, with advantages shown through numerical experiments.

Contribution

It proposes a new two-phase quasi-Newton scheme with proven convergence properties and improved performance over traditional methods.

Findings

Global convergence under mild assumptions

Superlinear convergence near the solution

Numerical results show improved efficiency

Abstract

In this paper, a two-phase quasi-Newton scheme is proposed for solving an unconstrained optimization problem. The global convergence property of the scheme is provided under mild assumptions. The superlinear rate of the scheme is also proved in the vicinity of the solution. The advantages of the proposed scheme over the traditional scheme are justified with numerical table and graphical illustrations.