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

2017/02/14 by Harry Oviedo, Oviedo, Harry, Hugo Lara +3
Computer Science · Mathematics · #Advanced Multi-Objective Optimization Algorithms #Advanced Optimization Algorithms Research #FOS: Mathematics #Metaheuristic Optimization Algorithms Research #Optimization and Control (math.OC)

paper · pdf · doi:10.48550/arxiv.1702.04303

openalex publication_date 2017/02/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Sparse Principal Component Analysis
• A Generalized Solution of the Orthogonal Procrustes Problem
• Generalized power method for sparse principal component analysis
• Numerical optimization

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