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Maximum-entropy samplingalgorithms and application /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Maximum-entropy samplingby Marcia Fampa, Jon Lee.
其他題名:	algorithms and application /
作者:	Fampa, Marcia.
其他作者:	Lee, Jon.
出版者:	Cham :Springer International Publishing :2022.
面頁冊數:	xvii, 195 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
標題:	Mathematical optimization.
電子資源:	https://doi.org/10.1007/978-3-031-13078-6
ISBN:	9783031130786$q(electronic bk.)

Maximum-entropy samplingalgorithms and application /
Fampa, Marcia.

Maximum-entropy samplingalgorithms and application /[electronic resource] :by Marcia Fampa, Jon Lee. - Cham :Springer International Publishing :2022. - xvii, 195 p. :ill., digital ;24 cm. - Springer series in operations research and financial engineering,2197-1773. - Springer series in operations research and financial engineering..

Overview -- Notation -- The problem and basic properties -- Branch-and-bound -- Upper bounds -- Environmental monitoring -- Opportunities -- Basic formulae and inequalities -- References -- Index.

This monograph presents a comprehensive treatment of the maximum-entropy sampling problem (MESP), which is a fascinating topic at the intersection of mathematical optimization and data science. The text situates MESP in information theory, as the algorithmic problem of calculating a sub-vector of pre-specificed size from a multivariate Gaussian random vector, so as to maximize Shannon's differential entropy. The text collects and expands on state-of-the-art algorithms for MESP, and addresses its application in the field of environmental monitoring. While MESP is a central optimization problem in the theory of statistical designs (particularly in the area of spatial monitoring), this book largely focuses on the unique challenges of its algorithmic side. From the perspective of mathematical-optimization methodology, MESP is rather unique (a 0/1 nonlinear program having a nonseparable objective function), and the algorithmic techniques employed are highly non-standard. In particular, successful techniques come from several disparate areas within the field of mathematical optimization; for example: convex optimization and duality, semidefinite programming, Lagrangian relaxation, dynamic programming, approximation algorithms, 0/1 optimization (e.g., branch-and-bound), extended formulation, and many aspects of matrix theory. The book is mainly aimed at graduate students and researchers in mathematical optimization and data analytics.

ISBN: 9783031130786$q(electronic bk.)

Standard No.: 10.1007/978-3-031-13078-6doiSubjects--Topical Terms:

183292
Mathematical optimization.

LC Class. No.: QA402.5 / .F35 2022

Dewey Class. No.: 519.6

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520 $a This monograph presents a comprehensive treatment of the maximum-entropy sampling problem (MESP), which is a fascinating topic at the intersection of mathematical optimization and data science. The text situates MESP in information theory, as the algorithmic problem of calculating a sub-vector of pre-specificed size from a multivariate Gaussian random vector, so as to maximize Shannon's differential entropy. The text collects and expands on state-of-the-art algorithms for MESP, and addresses its application in the field of environmental monitoring. While MESP is a central optimization problem in the theory of statistical designs (particularly in the area of spatial monitoring), this book largely focuses on the unique challenges of its algorithmic side. From the perspective of mathematical-optimization methodology, MESP is rather unique (a 0/1 nonlinear program having a nonseparable objective function), and the algorithmic techniques employed are highly non-standard. In particular, successful techniques come from several disparate areas within the field of mathematical optimization; for example: convex optimization and duality, semidefinite programming, Lagrangian relaxation, dynamic programming, approximation algorithms, 0/1 optimization (e.g., branch-and-bound), extended formulation, and many aspects of matrix theory. The book is mainly aimed at graduate students and researchers in mathematical optimization and data analytics.
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