Two adaptive scaled gradient projection methods for Stiefel manifold constrained optimization

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...

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Vydáno v:	Numerical algorithms Ročník 87; číslo 3; s. 1107 - 1127
Hlavní autoři:	Oviedo, Harry, Dalmau, Oscar, Lara, Hugo
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	New York Springer US 01.07.2021 Springer Nature B.V
Témata:	Algebra Algorithms Computer Science Convergence Eigenvalues Euclidean space Iterative algorithms Iterative methods Lagrange multiplier Manifolds (mathematics) Methods Numeric Computing Numerical Analysis Operators (mathematics) Optimization Original Paper Theory of Computation 65K05 Equality-constrained optimization Barzilai-Borwein-like method Gradient projection method 90C26 90C27 Nonmonotone line search Orthogonality constraint 90C30 Stiefel manifold 90C22 Spherical constraint Nonlinear programming 49Q99 Riemannian constrained optimization
ISSN:	1017-1398, 1572-9265
On-line přístup:	Získat plný text
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Shrnutí:	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.
Bibliografie:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14
ISSN:	1017-1398 1572-9265
DOI:	10.1007/s11075-020-01001-9