On efficiency of nonmonotone Armijo-type line searches

TL;DR

This paper investigates the efficiency of nonmonotone Armijo-type line searches in nonlinear optimization, proposing new nonmonotone terms, proving their convergence, and demonstrating their practical performance in solving unconstrained problems and inverse signal/image processing tasks.

Contribution

The paper introduces two novel nonmonotone terms for Armijo line searches, proves their global convergence, and evaluates their effectiveness through extensive numerical experiments.

Findings

Nonmonotone Armijo schemes outperform traditional methods in certain optimization tasks.

The proposed schemes successfully solve inverse problems in signal and image processing.

Numerical results show improved convergence and computational efficiency.

Abstract

Monotonicity and nonmonotonicity play a key role in studying the global convergence and the efficiency of iterative schemes employed in the field of nonlinear optimization, where globally convergent and computationally efficient schemes are explored. This paper addresses some features of descent schemes and the motivation behind nonmonotone strategies and investigates the efficiency of an Armijo-type line search equipped with some popular nonmonotone terms. More specifically, we propose two novel nonmonotone terms, combine them into Armijo's rule and establish the global convergence of sequences generated by these schemes. Furthermore, we report extensive numerical results and comparisons indicating the performance of the nonmonotone Armijo-type line searches using the most popular search directions for solving unconstrained optimization problems. Finally, we exploit the considered nonmonotone schemes to solve an important inverse problem arising in signal and image processing.