TY - GEN
T1 - A Scaled Gradient Projection Method for Minimization over the Stiefel Manifold
AU - Oviedo, Harry
AU - Dalmau, Oscar
N1 - Publisher Copyright:
© Springer Nature Switzerland AG 2019.
PY - 2019
Y1 - 2019
N2 - In this paper we consider a class of iterative gradient projection methods for solving optimization problems with orthogonality constraints. The proposed method can be seen as a forward-backward gradient projection method which is an extension of a gradient method based on the Cayley transform. The proposal incorporates a self-adaptive scaling matrix and the Barzilai-Borwein step-sizes that accelerate the convergence of the method. In order to preserve feasibility, we adopt a projection operator based on the QR factorization. We demonstrate the efficiency of our procedure in several test problems including eigenvalue computations and sparse principal component analysis. Numerical comparisons show that our proposal is effective for solving these kind of problems and presents competitive results compared with some state-of-art methods.
AB - In this paper we consider a class of iterative gradient projection methods for solving optimization problems with orthogonality constraints. The proposed method can be seen as a forward-backward gradient projection method which is an extension of a gradient method based on the Cayley transform. The proposal incorporates a self-adaptive scaling matrix and the Barzilai-Borwein step-sizes that accelerate the convergence of the method. In order to preserve feasibility, we adopt a projection operator based on the QR factorization. We demonstrate the efficiency of our procedure in several test problems including eigenvalue computations and sparse principal component analysis. Numerical comparisons show that our proposal is effective for solving these kind of problems and presents competitive results compared with some state-of-art methods.
KW - Gradient projection method
KW - Nonlinear programming
KW - Orthogonality constraints
KW - Stiefel manifold
UR - http://www.scopus.com/inward/record.url?scp=85075666513&partnerID=8YFLogxK
U2 - 10.1007/978-3-030-33749-0_20
DO - 10.1007/978-3-030-33749-0_20
M3 - Conference contribution
AN - SCOPUS:85075666513
SN - 9783030337483
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 239
EP - 250
BT - Advances in Soft Computing - 18th Mexican International Conference on Artificial Intelligence, MICAI 2019, Proceedings
A2 - Martínez-Villaseñor, Lourdes
A2 - Batyrshin, Ildar
A2 - Marín-Hernández, Antonio
PB - Springer
T2 - 18th Mexican International Conference on Artificial Intelligence, MICAI 2019
Y2 - 27 October 2019 through 2 November 2019
ER -