TY - JOUR
T1 - Two adaptive scaled gradient projection methods for Stiefel manifold constrained optimization
AU - Oviedo, Harry
AU - Dalmau, Oscar
AU - Lara, Hugo
N1 - Funding Information:
The second author wants to thank the Federal University of Santa Catarina–Brazil and remarks that his contribution to the present article was predominantly carried out at this institution.
Funding Information:
This research was supported in part by Conacyt, Mexico (258033 research grant and H.O.L. PhD. studies scholarship). Acknowledgements
Publisher Copyright:
© 2020, Springer Science+Business Media, LLC, part of Springer Nature.
PY - 2021/7
Y1 - 2021/7
N2 - This article is concerned with the problem of minimizing a smooth function over the Stiefel manifold. In order to address this problem, we introduce two adaptive scaled gradient projection methods that incorporate scaling matrices that depend on the step-size and a parameter that controls the search direction. These iterative algorithms use a projection operator based on the QR factorization to preserve the feasibility in each iteration. However, for some particular cases, the proposals do not require the use of any projection operator. In addition, we consider a Barzilai and Borwein-like step-size combined with the Zhang–Hager nonmonotone line-search technique in order to accelerate the convergence of the proposed procedures. We proved the global convergence for these schemes, and we evaluate their effectiveness and efficiency through an extensive computational study, comparing our approaches with other state-of-the-art gradient-type algorithms.
AB - This article is concerned with the problem of minimizing a smooth function over the Stiefel manifold. In order to address this problem, we introduce two adaptive scaled gradient projection methods that incorporate scaling matrices that depend on the step-size and a parameter that controls the search direction. These iterative algorithms use a projection operator based on the QR factorization to preserve the feasibility in each iteration. However, for some particular cases, the proposals do not require the use of any projection operator. In addition, we consider a Barzilai and Borwein-like step-size combined with the Zhang–Hager nonmonotone line-search technique in order to accelerate the convergence of the proposed procedures. We proved the global convergence for these schemes, and we evaluate their effectiveness and efficiency through an extensive computational study, comparing our approaches with other state-of-the-art gradient-type algorithms.
KW - Barzilai-Borwein-like method
KW - Equality-constrained optimization
KW - Gradient projection method
KW - Nonlinear programming
KW - Nonmonotone line search
KW - Orthogonality constraint
KW - Riemannian constrained optimization
KW - Spherical constraint
KW - Stiefel manifold
UR - http://www.scopus.com/inward/record.url?scp=85089964410&partnerID=8YFLogxK
U2 - 10.1007/s11075-020-01001-9
DO - 10.1007/s11075-020-01001-9
M3 - Article
AN - SCOPUS:85089964410
SN - 1017-1398
VL - 87
SP - 1107
EP - 1127
JO - Numerical Algorithms
JF - Numerical Algorithms
IS - 3
ER -