Global convergence of the Armijo epsilon steepest descent algorithm

Abstract

In this article, we study the unconstrained minimization problem\[(P)\,\,\,\min\left\{ f(x):x\in\mathbb{R}^{n}\right\} .\]where \(f:\mathbb{R}^{n}\rightarrow\mathbb{R}\) is a continuously differentiable function. We introduce a new algorithm which accelerates the convergence of the steepest descent method. We further establish the global convergence of this algorithm in the case of Armijo inexact line search.

Keywords

• unconstrained optimization
• global convergence
• steepest descent algorithm
• \( \varepsilon\)-algorithm
• Armijo inexact line search