# A Non-monotone Linear Search Method with Mixed Direction on Stiefel Manifold

## TL;DR

This paper introduces a novel non-monotone line search algorithm for optimization on the Stiefel manifold, combining mixed gradients and Barzilai-Borwein steps, with theoretical analysis and numerical comparisons.

## Contribution

It presents a new non-monotone line search method utilizing mixed gradients and SVD-based projections for optimization on Stiefel manifolds, enhancing existing techniques.

## Key findings

- Algorithm converges reliably on test problems.
- Numerical results show improved performance over existing methods.
- Theoretical analysis confirms convergence properties.

## Abstract

In this paper, we propose a non-monotone line search method for solving optimization problems on Stiefel manifold. Our method uses as a search direction a mixed gradient based on a descent direction, and a Barzilai-Borwein line search. Feasibility is guaranteed by projecting each iterate on the Stiefel manifold, through SVD factorizations. Some theoretical results for analyzing the algorithm are presented. Finally, we provide numerical experiments comparing our algorithm with other state-of-the-art procedures.