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Accelerated First-Order Optimization with Orthogonality Constraints
Başlık:
Accelerated First-Order Optimization with Orthogonality Constraints
Yazar:
Siegel, Jonathan Wolfram, author.
ISBN:
9780438009738
Yazar Ek Girişi:
Fiziksel Tanımlama:
1 electronic resource (90 pages)
Genel Not:
Source: Dissertation Abstracts International, Volume: 79-10(E), Section: B.
Includes supplementary digital materials.
Advisors: Russel E. Caflisch Committee members: Chris Anderson; Stanley Osher; Vidvuds Ozolins.
Özet:
Optimization problems with orthogonality constraints have many applications in science and engineering. In these applications, one often deals with large-scale problems which are ill-conditioned near the optimum. Consequently, there is a need for first-order optimization methods which deal with orthogonality constraints, converge rapidly even when the objective is not well-conditioned, and are robust.
In this dissertation we develop a generalization of Nesterov's accelerated gradient descent algorithm for optimization on the manifold of orthonormal matrices. The performance of the algorithm scales with the square root of the condition number. As a result, our method outperforms existing state-of-the-art algorithms on large, ill-conditioned problems. We discuss applications of the method to electronic structure calculations and to the calculation of compressed modes.
Notlar:
School code: 0031
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Yer Numarası | Demirbaş Numarası | Shelf Location | Lokasyon / Statüsü / İade Tarihi |
---|---|---|---|
XX(682225.1) | 682225-1001 | Proquest E-Tez Koleksiyonu | Arıyor... |
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