Entropy Optimization and Mathematical Programming

1997
ISBN: 978-0-7923-9939-1
Verlag: Springer US

Buch, Englisch, Band 8, 343 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 1500 g

Reihe: International Series in Operations Research & Management Science

Entropy optimization is a useful combination of classical engineering theory with mathematical optimization. The resulting 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. offers perspectives that meet the needs of diverse so that the users can apply 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.

Zielgruppe

Research

Autoren/Hrsg.

Tsao, H. S. J.

Rajasekera, J.R.

Fachgebiete

• Wirtschaftswissenschaften Betriebswirtschaft Wirtschaftsmathematik und -statistik
• Wirtschaftswissenschaften Betriebswirtschaft Unternehmensforschung
• Wirtschaftswissenschaften Volkswirtschaftslehre Volkswirtschaftslehre Allgemein Ökonometrie
• Mathematik | Informatik Mathematik Mathematische Analysis Variationsrechnung
• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung
• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik
• Mathematik | Informatik Mathematik Operations Research Spieltheorie

Inhaltsverzeichnis

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.