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Optimization over Digraphs: Linear Algorithms with Linear Convergence
Başlık:
Optimization over Digraphs: Linear Algorithms with Linear Convergence
Yazar:
Xin, Ran, author.
ISBN:
9780438021044
Yazar Ek Girişi:
Fiziksel Tanımlama:
1 electronic resource (53 pages)
Genel Not:
Source: Masters Abstracts International, Volume: 57-06M(E).
Advisors: Usman A. Khan Committee members: Babak Moaveni; Brian H. Tracey.
Özet:
In this thesis, we study distributed optimization, where a network of agents, interacting over a directed graph, collaborates to minimize the average of locally-known convex functions. Most of the existing algorithms apply push-sum consensus, which utilizes column-stochastic weight matrices. Column-stochastic weights require each agent to know (at least) its out degree, which may be impractical in e.g., broadcast-based communication protocols. In contrast, we describe FROST (Fast Row-stochastic Optimization with uncoordinated STep-sizes), an optimization algorithm applicable to directed graphs with row-stochastic weights and non-identical step-sizes at the agents. Its implementation is straightforward as each agent locally decides the weights assigned to the incoming information and locally chooses a suitable step-size. Furthermore, we propose a completely linear algorithm which avoids using push-sum (type) techniques and thus leads to less communication and computation over the network of agents. Under the assumptions that each local function is strongly-convex with Lipschitz-continuous gradients, we show that the proposed algorithms linearly converge to the global minimizer with sufficiently small step-sizes. We present numerical simulations to illustrate our theoretical results.
Notlar:
School code: 0234
Konu Başlığı:
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Yer Numarası | Demirbaş Numarası | Shelf Location | Lokasyon / Statüsü / İade Tarihi |
---|---|---|---|
XX(692323.1) | 692323-1001 | Proquest E-Tez Koleksiyonu | Arıyor... |
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