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Some Results on a Class of Functiona...
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Dewhurst, David Rushing.
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Some Results on a Class of Functional Optimization Problems.
紀錄類型:
書目-電子資源 : Monograph/item
正題名/作者:
Some Results on a Class of Functional Optimization Problems./
作者:
Dewhurst, David Rushing.
出版者:
Ann Arbor : ProQuest Dissertations & Theses, : 2018,
面頁冊數:
60 p.
附註:
Source: Masters Abstracts International, Volume: 57-05.
Contained By:
Masters Abstracts International57-05(E).
標題:
Mathematics. -
電子資源:
http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10786670
ISBN:
9780355832488
Some Results on a Class of Functional Optimization Problems.
Dewhurst, David Rushing.
Some Results on a Class of Functional Optimization Problems.
- Ann Arbor : ProQuest Dissertations & Theses, 2018 - 60 p.
Source: Masters Abstracts International, Volume: 57-05.
Thesis (M.S.)--The University of Vermont and State Agricultural College, 2018.
We first describe a general class of optimization problems that describe many natu- ral, economic, and statistical phenomena. After noting the existence of a conserved quantity in a transformed coordinate system, we outline several instances of these problems in statistical physics, facility allocation, and machine learning. A dynamic description and statement of a partial inverse problem follow. When attempting to optimize the state of a system governed by the generalized equipartitioning princi- ple, it is vital to understand the nature of the governing probability distribution. We show that optimiziation for the incorrect probability distribution can have catas- trophic results, e.g., infinite expected cost, and describe a method for continuous Bayesian update of the posterior predictive distribution when it is stationary. We also introduce and prove convergence properties of a time-dependent nonparametric kernel density estimate (KDE) for use in predicting distributions over paths. Finally, we extend the theory to the case of networks, in which an event probability density is defined over nodes and edges and a system resource is to be partitioning among the nodes and edges as well. We close by giving an example of the theory's application by considering a model of risk propagation on a power grid.
ISBN: 9780355832488Subjects--Topical Terms:
515831
Mathematics.
Some Results on a Class of Functional Optimization Problems.
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