Hierarchical Optimization and Mathematical Physics

By: Vladimir Tsurkov

Write A Review

Hardcover | 1 December 2009

At a Glance

Hardcover
324 Pages

Dimensions(cm)
24.13 x 16.51 x 2.54

Hardcover

$169.00

or 4 interest-free payments of $42.25 with

Ships in 5 to 7 business days

This book should be considered as an introduction to a special dass 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 problern with macrovariables, whose number is less than the number of initial variables. This problern is often very simple. On the lower level, we have the usual optimal control problems of math ematical physics, which are far simpler than the initial statements. Thus, the decomposition (or reduction to problems ofless dimensions) is obtained. The algorithm constructs a sequence of so-called disaggregated solutions that are feasible for the main problern and converge to its optimal solutionunder certain assumptions ( e.g., under strict convexity of the input functions). 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 preset assortment relation. The ratio coefficient is maximized. Constraints are given in the form of linear inequalities with block diagonal structure of the part of a matrix that corresponds to subsystems. The central coordinator assem bles the final production from the components produced by the subsystems.

Shipping

	Standard Shipping	Express Shipping
Metro postcodes:	$9.99	$14.95
Regional postcodes:	$9.99	$14.95
Rural postcodes:	$9.99	$14.95

Orders over $79.00 qualify for free shipping.

How to return your order

At Booktopia, we offer hassle-free returns in accordance with our returns policy. If you wish to return an item, please get in touch with Booktopia Customer Care.

Additional postage charges may be applicable.

Defective items

If there is a problem with any of the items received for your order then the Booktopia Customer Care team is ready to assist you.

For more info please visit our Help Centre.

You Can Find This Book In

Non-Fiction Science Physics Mathematical Physics Mathematics Optimisation Game Theory Science in General Maths for Scientists Applied Mathematics Nonlinear Science Linear Programming

Reference, Information & Interdisciplinary Subjects Research & Information Information theory Cybernetics & Systems Theory

Other Editions and Formats

Paperback

Published: 15th November 2013

View Product

Preface
The Main Model and Constructions of the Decomposition Method	p. 1
Necessary Knowledge from the Theory of Extremal Problems	p. 2
Branch Model and Description of the Algorithm	p. 14
Optimality Criterion and the Aggregated Problem	p. 20
Local Monotonicity with Respect to the Functional and Numerical Computation	p. 27
Modification of the Main Model	p. 33
Random Parameters in the Branch Model	p. 47
Comments and References to Chapter 1	p. 59
Generalization of the Decomposition Approach to Mathematical Programming and Classical Calculus of Variations	p. 62
Linear Programming	p. 62
Quadratic Programming	p. 69
Mathematical Programming	p. 76
Classical Calculus of Variations	p. 84
Comments and References to Chapter 2	p. 97
Hierarchical Systems of Mathematical Physics	p. 99
Construction of the Method for Block Separable Problems of Optimal Control	p. 99
Analytical Examples	p. 113
Block Problems of Optimal Control with Partial Differential Equations	p. 125
Linear-Quadratic Optimal Control Problems of Block Type	p. 146
Comments and References to Chapter 3	p. 155
Effectiveness of Decomposition	p. 158
Nonlinear Two-level Statements	p. 158
Models of Hierarchical Systems with Distributed Parameters	p. 174
Block Separable Problems with Large Number of Binding Constraints	p. 189
Nonseparable Functionals	p. 200
Results of Numerical Computation	p. 212
Comments and References to Chapter 4	p. 224
Appendix. The Main Approaches in Hierarchical Optimization	p. 226
Dantzig-Wolfe Principle	p. 226
Kornai-Liptak Principle	p. 235
Parametric Decomposition	p. 256
Iterative Aggregation	p. 262
The Use of Lagrange Functional in Block Dynamical Problems	p. 276
Comments and References of Chapter 5	p. 297
Index	p. 304
Table of Contents provided by Blackwell. All Rights Reserved.

Hierarchical Optimization and Mathematical Physics

At a Glance

Hardcover

Shipping

How to return your order

Defective items

You Can Find This Book In

Other Editions and Formats

Paperback

More in Linear Programming

Statistical Analysis with R For Dummies

For Dummies (Computer/Tech)

Elementary Linear Algebra

8th Edition - International Metric Edition

Iterative Methods for Linear and Nonlinear Equations

Frontiers in Applied Mathematics

Linear Algebra for Localization

Algorithms, Use Cases, and C++ Implementations

Fuzzy-Model-Based Mode Control of Complex Nonlinear Systems

Engineering Mathematics and Operations Research

The Official Raspberry Pi Handbook 2026

Astounding projects with Raspberry Pi computers

NONLINEAR WORKBOOK (6TH ED)

Chaos, Fractals, Cellular Automata, Genetic Algorithms, Gene Expression Programming, Support Vector Machine, Wavelets, Hidden Markov Models, Fuzzy Logic With C++, Java And Symbolicc++ Programs (6th Edition)

Integral and Integro-Differential Equations

Wavelet-Based Numerical Methods

Advances on Mathematical Modeling and Optimization with Its Applications

Emerging Technologies

Statistical Modeling and Applications on Real-Time Problems

Enhancing Understanding and Practical Implementation

Statistical Modeling and Applications on Real-Time Problems

Unraveling Insights through Advanced Analytical Techniques

DYNAMICS, CONTROL, AND SYNCHRONIZATION OF NONLINEAR SYSTEMS

Theory of Oscillations

Series on Optimization

Minimax Models in the Theory of Numerical Methods

Theory and Decision Library

Neural Network for Optimization and Combinatorics

Oscillation Theory of Operator - Differential Equations

Series on Soviet and East European Mathematics

Recent Advances in Nonsmooth Optimization

Totally Convex Functions for Fixed Points Computation

Applied Optimization

Inequality Theory and Applications

Combinatorial and Global Optimization

Series on Applied Mathematics

Nonlinear Workbook, The

Chaos, Fractals, Cellular Automata, Neural Networks, Genetic Algorithms, Gene Expression Programming, Wavelets, Fuzzy Logic With C++, Java And Symbolic C++ Programs (2nd Edition)

Selected Papers of Alan J. Hoffman : With Commentary

With Commentary

Nonlinear Dynamics : From Lasers to Butterflies

From Lasers to Butterflies

An Introduction to Natural Computation

Bradford Books

This product is categorised by