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＜電子ブック＞
Maximum-Entropy Sampling : Algorithms and Application / by Marcia Fampa, Jon Lee
(Springer Series in Operations Research and Financial Engineering. ISSN:21971773)

版	1st ed. 2022.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2022
本文言語	英語
大きさ	XVII, 195 p. 10 illus., 9 illus. in color : online resource
著者標目	*Fampa, Marcia author Lee, Jon author SpringerLink (Online service)
件　名	LCSH:Mathematical optimization LCSH:Operations research LCSH:Management science FREE:Optimization FREE:Operations Research, Management Science
一般注記	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. HTTP:URL=https://doi.org/10.1007/978-3-031-13078-6

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