Entropy Optimization and Mathematical Programming by H.S.J. Tsao (English) Paper

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Entropy Optimization and Mathematical Programming by H.S.J. Tsao, J.R. Rajasekera, Shu-Cherng Fang

Entropy optimization is a useful combination of classical engineering theory (entropy) with mathematical optimization.

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Paperback LANGUAGE
English CONDITION
Brand New Publisher Description

Entropy optimization is a useful combination of classical engineering theory (entropy) with mathematical optimization. The resulting entropy optimization models have proved their usefulness with successful applications in areas such as image reconstruction, pattern recognition, statistical inference, queuing theory, spectral analysis, statistical mechanics, transportation planning, urban and regional planning, input-output analysis, portfolio investment, information analysis, and linear and nonlinear programming.
While entropy optimization has been used in different fields, a good number of applicable solution methods have been loosely constructed without sufficient mathematical treatment. A systematic presentation with proper mathematical treatment of this material is needed by practitioners and researchers alike in all application areas. The purpose of this book is to meet this need. Entropy Optimization and Mathematical Programming offers perspectives that meet the needs of diverse user communities so that the users can apply entropy optimization techniques with complete comfort and ease. With this consideration, the authors focus on the entropy optimization problems in finite dimensional Euclidean space such that only some basic familiarity with optimization is required of the reader.

Table of Contents

1 Introduction to Entropy and Entropy Optimization Principles.- 1.1 Introduction to Finite-Dimensional Entropy.- 1.2 Entropy Optimization Problems.- References.- 2 Entropy Optimization Models.- 2.1 Queueing Theory.- 2.2 Transportation Planning.- 2.3 Input-Output Analysis.- 2.4 Regional Planning.- 2.5 Portfolio Optimization.- 2.6 Image Reconstruction.- References.- 3 Entropy Optimization Methods: Linear Case.- 3.1 Existing Methods.- 3.2 An Unconstrained Convex Programming Approach.- 3.3 Entropy Optimization Problems with Infinitely Many Linear Constraints.- References.- 4 Entropy Optimization Methods: General Convex Case.- 4.1 Existing Methods.- 4.2 Entropy Optimization with Quadratic Constraints.- 4.3 Entropy Optimization with Entropic Constraints.- 4.4 Entropy Optimization with Convex Constraints.- References.- 5 Entropic Perturbation Approach to Mathematical Programming.- 5.1 Linear Programming: Karmarkar-Form.- 5.2 Linear Programming: Standard-Form.- 5.3 Convex Quadratic Programming.- 5.4 Linear and Convex Quadratic Semi-infinite Programming.- References.- 6 Lp-Norm Perturbation Approach: A Generalization of Entropic Perturbation.- 6.1 Perturbing the Dual Feasible Region of Standard-form Linear Programs.- 6.2 Solving Linear Programs with Inequality Constraints via Perturbation of Feasible Region.- 6.3 Perturbing Dual Feasible Region of Convex Quadratic Programs.- References.- 7 Extensions and Related Results.- 7.1 Entropy Optimization with Countably Many Variables.- 7.2 Entropy Optimization and Bayesian Statistical Estimation.- 7.3 Entropic Regularization for Min-Max Problems.- 7.4 Semi-Infinite Min-Max Problems.- References.

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Long Description

Entropy optimization is a useful combination of classical engineering theory (entropy) with mathematical optimization. The resulting entropy optimization models have proved their usefulness with successful applications in areas such as image reconstruction, pattern recognition, statistical inference, queuing theory, spectral analysis, statistical mechanics, transportation planning, urban and regional planning, input-output analysis, portfolio investment, information analysis, and linear and nonlinear programming. While entropy optimization has been used in different fields, a good number of applicable solution methods have been loosely constructed without sufficient mathematical treatment. A systematic presentation with proper mathematical treatment of this material is needed by practitioners and researchers alike in all application areas. The purpose of this book is to meet this need. Entropy Optimization and Mathematical Programming offers perspectives that meet the needs of diverse user communities so that the users can apply entropy optimization techniques with complete comfort and ease. With this consideration, the authors focus on the entropy optimization problems in finite dimensional Euclidean space such that only some basic familiarity with optimization is required of the reader.

Details ISBN1461378109 Author Shu-Cherng Fang Language English Edition 97199th ISBN-10 1461378109 ISBN-13 9781461378105 Series International Series in Operations Research & Management Science Media Book Series Number 8 Short Title ENTROPY OPTIMIZATION & MATHEMA Year 2012 Publication Date 2012-10-29 Imprint Springer-Verlag New York Inc. Place of Publication New York, NY Country of Publication United States DEWEY 515.64 Illustrations X, 343 p. AU Release Date 2012-10-29 NZ Release Date 2012-10-29 US Release Date 2012-10-29 UK Release Date 2012-10-29 Pages 343 Publisher Springer-Verlag New York Inc. Edition Description Softcover reprint of the original 1st ed. 1997 Format Paperback Alternative 9780792399391 Audience Professional & Vocational Country of Origin NL Product Class Description Mathematics
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