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Hierarchical Optimization and Mathematical Physics : Applied Optimization - Vladimir Tsurkov

Hierarchical Optimization and Mathematical Physics

Applied Optimization

Hardcover Published: December 2009
ISBN: 9780792361756
Number Of Pages: 310

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This book should be considered as an introduction to a special class of hierarchical systems of optimal control, where subsystems are described by partial differential equations of various types. Optimization is carried out by means of a two-level scheme, where the center optimizes coordination for the upper level and subsystems find the optimal solutions for independent local problems. The main algorithm is a method of iterative aggregation. The coordinator solves the problem with macrovariables, whose number is less than the number of initial variables. On the lower level, we have the usual optimal control problems of mathematical physics, which are far simpler than the initial statements. Thus, we bridge the gap between two disciplines: optimization theory of large-scale systems and mathematical physics. The first motivation was a special model of branch planning, where the final product obeys a precept assortment relation. Audience: The monograph is addressed to specialists in operations research, optimization, optimal control, and mathematical physics.

The Main Model and Constructions of the Decomposition Methodp. 1
Necessary Knowledge from the Theory of Extremal Problemsp. 2
Branch Model and Description of the Algorithmp. 14
Optimality Criterion and the Aggregated Problemp. 20
Local Monotonicity with Respect to the Functional and Numerical Computationp. 27
Modification of the Main Modelp. 33
Random Parameters in the Branch Modelp. 47
Comments and References to Chapter 1p. 59
Generalization of the Decomposition Approach to Mathematical Programming and Classical Calculus of Variationsp. 62
Linear Programmingp. 62
Quadratic Programmingp. 69
Mathematical Programmingp. 76
Classical Calculus of Variationsp. 84
Comments and References to Chapter 2p. 97
Hierarchical Systems of Mathematical Physicsp. 99
Construction of the Method for Block Separable Problems of Optimal Controlp. 99
Analytical Examplesp. 113
Block Problems of Optimal Control with Partial Differential Equationsp. 125
Linear-Quadratic Optimal Control Problems of Block Typep. 146
Comments and References to Chapter 3p. 155
Effectiveness of Decompositionp. 158
Nonlinear Two-level Statementsp. 158
Models of Hierarchical Systems with Distributed Parametersp. 174
Block Separable Problems with Large Number of Binding Constraintsp. 189
Nonseparable Functionalsp. 200
Results of Numerical Computationp. 212
Comments and References to Chapter 4p. 224
Appendix. The Main Approaches in Hierarchical Optimizationp. 226
Dantzig-Wolfe Principlep. 226
Kornai-Liptak Principlep. 235
Parametric Decompositionp. 256
Iterative Aggregationp. 262
The Use of Lagrange Functional in Block Dynamical Problemsp. 276
Comments and References of Chapter 5p. 297
Indexp. 304
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780792361756
ISBN-10: 079236175X
Series: Applied Optimization
Audience: General
Format: Hardcover
Language: English
Number Of Pages: 310
Published: December 2009
Publisher: Springer
Country of Publication: NL
Dimensions (cm): 23.39 x 15.6  x 1.91
Weight (kg): 0.63

Earn 456 Qantas Points
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