A Generalized Worst-Case Complexity Analysis for Non-Monotone Line Searches

TL;DR

This paper provides a comprehensive worst-case complexity analysis for a broad class of non-monotone line search algorithms, extending understanding of their efficiency even with non-summable non-monotonicity controls.

Contribution

It introduces a generalized framework for non-monotone line searches and derives complexity bounds applicable without the summability condition on non-monotonicity parameters.

Findings

Complexity bounds established for non-monotone line searches.

Analysis applies even when non-monotonicity parameters are not summable.

Framework encompasses many existing line search techniques.

Abstract

We study the worst-case complexity of a non-monotone line search framework that covers a wide variety of known techniques published in the literature. In this framework, the non-monotonicity is controlled by a sequence of nonnegative parameters. We obtain complexity bounds to achieve approximate first-order optimality even when this sequence is not summable.