The Performance of MBFGS with Different Inexact Line Search Rule

TL;DR

This paper evaluates the performance of the modified BFGS optimization algorithm using various inexact line search methods, highlighting the efficiency of Armijo line search in solving non-convex nonlinear problems.

Contribution

It compares different inexact line search strategies within MBFGS, demonstrating Armijo's method as particularly effective for non-convex optimization.

Findings

MBFGS with Armijo line search outperforms other methods in efficiency.

Numerical results confirm Armijo's suitability for non-convex problems.

Different line search methods significantly impact optimization performance.

Abstract

The modified BFGS optimization algorithm is generally used when the objective function is non-convex. In this method, one has to move in a specific direction such that the value of the objective function reduces. Therefore, the different inexact line search or exact line search plays an important role in optimization. Here, we have studied Modified BFGS with different inexact line searches methods and compared them in some test problems. Numerical results show that MBFGS with Armijo line search methods is efficient for solving non-convex non-linear unconstrained optimization problems.