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E-raamat: Optimization in Engineering Sciences: Exact Methods

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  • Formaat: PDF+DRM
  • Ilmumisaeg: 24-Jan-2013
  • Kirjastus: ISTE Ltd and John Wiley & Sons Inc
  • Keel: eng
  • ISBN-13: 9781118577752
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Optimization in Engineering Sciences: Exact MethodsSuurem pilt
  • Formaat: PDF+DRM
  • Ilmumisaeg: 24-Jan-2013
  • Kirjastus: ISTE Ltd and John Wiley & Sons Inc
  • Keel: eng
  • ISBN-13: 9781118577752
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The purpose of this book is to present the main methods of static and dynamic optimization. It has been written within the framework of the European Union project – ERRIC (Empowering Romanian Research on Intelligent Information Technologies), funded by the EU’s FP7 Research Potential program and developed in cooperation between French and Romanian teaching researchers.
Through the principles of various proposed algorithms (with additional references) this book allows the interested reader to explore various methods of implementation such as linear programming, nonlinear programming – particularly important given the wide variety of existing algorithms, dynamic programming with various application examples and Hopfield networks. The book examines optimization in relation to systems identification; optimization of dynamic systems with particular application to process control; optimization of large scale and complex systems; optimization and information systems.

Foreword ix
Preface xi
List of Acronyms
xiii
Chapter 1 Linear Programming
1(22)
1.1 Objective of linear programming
1(1)
1.2 Stating the problem
1(3)
1.3 Lagrange method
4(1)
1.4 Simplex algorithm
5(6)
1.4.1 Principle
5(1)
1.4.2 Simplicial form formulation
5(2)
1.4.3 Transition from one simplicial form to another
7(2)
1.4.4 Summary of the simplex algorithm
9(2)
1.5 Implementation example
11(2)
1.6 Linear programming applied to the optimization of resource allocation
13(10)
1.6.1 Areas of application
13(1)
1.6.2 Resource allocation for advertising
13(3)
1.6.3 Optimization of a cut of paper rolls
16(1)
1.6.4 Structure of linear program of an optimal control problem
17(6)
Chapter 2 Nonlinear Programming
23(78)
2.1 Problem formulation
23(1)
2.2 Karush--Kuhn--Tucker conditions
24(2)
2.3 General search algorithm
26(7)
2.3.1 Main steps
26(3)
2.3.2 Computing the search direction
29(4)
2.3.3 Computation of advancement step
33(1)
2.4 Monovariable methods
33(6)
2.4.1 Coggin's method (of polynomial interpolation)
34(2)
2.4.2 Golden section method
36(3)
2.5 Multivariable methods
39(62)
2.5.1 Direct search methods
39(18)
2.5.2 Gradient methods
57(44)
Chapter 3 Dynamic Programming
101(14)
3.1 Principle of dynamic programming
101(1)
3.1.1 Stating the problem
101(1)
3.1.2 Decision problem
101(1)
3.2 Recurrence equation of optimality
102(2)
3.3 Particular cases
104(3)
3.3.1 Infinite horizon stationary problems
104(1)
3.3.2 Variable horizon problem
104(1)
3.3.3 Random horizon problem
104(1)
3.3.4 Taking into account sum-like constraints
105(1)
3.3.5 Random evolution law
106(1)
3.3.6 Initialization when the final state is imposed
106(1)
3.3.7 The case when the necessary information is not always available
107(1)
3.4 Examples
107(8)
3.4.1 Route optimization
107(2)
3.4.2 The smuggler problem
109(6)
Chapter 4 Hopfield Networks
115(16)
4.1 Structure
115(2)
4.2 Continuous dynamic Hopfield networks
117(6)
4.2.1 General problem
117(4)
4.2.2 Application to the traveling salesman problem
121(2)
4.3 Optimization by Hopfield networks, based on simulated annealing
123(8)
4.3.1 Deterministic method
123(2)
4.3.2 Stochastic method
125(6)
Chapter 5 Optimization in System Identification
131(60)
5.1 The optimal identification principle
131(1)
5.2 Formulation of optimal identification problems
132(6)
5.2.1 General problem
132(1)
5.2.2 Formulation based on optimization theory
133(3)
5.2.3 Formulation based on estimation theory (statistics)
136(2)
5.3 Usual identification models
138(8)
5.3.1 General model
138(2)
5.3.2 Rational input/output (RIO) models
140(2)
5.3.3 Class of autoregressive models (ARMAX)
142(3)
5.3.4 Class of state space representation models
145(1)
5.4 Basic least squares method
146(12)
5.4.1 LSM type solution
146(5)
5.4.2 Geometric interpretation of the LSM solution
151(3)
5.4.3 Consistency of the LSM type solution
154(3)
5.4.4 Example of application of the LSM for an ARX model
157(1)
5.5 Modified least squares methods
158(10)
5.5.1 Recovering lost consistency
158(4)
5.5.2 Extended LSM
162(2)
5.5.3 Instrumental variables method
164(4)
5.6 Minimum prediction error method
168(7)
5.6.1 Basic principle and algorithm
168(3)
5.6.2 Implementation of the MPEM for ARMAX models
171(3)
5.6.3 Convergence and consistency of MPEM type estimations
174(1)
5.7 Adaptive optimal identification methods
175(16)
5.7.1 Accuracy/adaptability paradigm
175(2)
5.7.2 Basic adaptive version of the LSM
177(5)
5.7.3 Basic adaptive version of the IVM
182(1)
5.7.4 Adaptive window versions of the LSM and IVM
183(8)
Chapter 6 Optimization of Dynamic Systems
191(60)
6.1 Variational methods
191(5)
6.1.1 Variation of a functional
191(1)
6.1.2 Constraint-free minimization
192(2)
6.1.3 Hamilton canonical equations
194(1)
6.1.4 Second-order conditions
195(1)
6.1.5 Minimization with constraints
195(1)
6.2 Application to the optimal command of a continuous process, maximum principle
196(10)
6.2.1 Formulation
196(2)
6.2.2 Examples of implementation
198(8)
6.3 Maximum principle, discrete case
206(1)
6.4 Principle of optimal command based on quadratic criteria
207(3)
6.5 Design of the LQ command
210(14)
6.5.1 Finite horizon LQ command
210(7)
6.5.2 The infinite horizon QL command
217(4)
6.5.3 Robustness of the LQ command
221(3)
6.6 Optimal filtering
224(15)
6.6.1 Kalman--Bucy predictor
225(6)
6.6.2 Kalman--Bucy filter
231(3)
6.6.3 Stability of Kalman--Bucy estimators
234(1)
6.6.4 Robustness of Kalman--Bucy estimators
235(4)
6.7 Design of the LQG command
239(6)
6.8 Optimization problems connected to quadratic linear criteria
245(6)
6.8.1 Optimal control by state feedback
245(3)
6.8.2 Quadratic stabilization
248(1)
6.8.3 Optimal command based on output feedback
249(2)
Chapter 7 Optimization of Large-Scale Systems
251(38)
7.1 Characteristics of complex optimization problems
251(1)
7.2 Decomposition techniques
252(31)
7.2.1 Problems with block-diagonal structure
253(14)
7.2.2 Problems with separable criteria and constraints
267(16)
7.3 Penalization techniques
283(6)
7.3.1 External penalization technique
284(1)
7.3.2 Internal penalization technique
285(1)
7.3.3 Extended penalization technique
286(3)
Chapter 8 Optimization and Information Systems
289(10)
8.1 Introduction
289(1)
8.2 Factors influencing the construction of IT systems
290(2)
8.3 Approaches
292(4)
8.4 Selection of computing tools
296(1)
8.5 Difficulties in implementation and use
297(1)
8.6 Evaluation
297(1)
8.7 Conclusions
298(1)
Bibliography 299(8)
Index 307
Pierre Borne is Professor "de Classe Exceptionnelle" at the Ecole Centrale de Lille, France.

Dumitru Popescu is Professor at the Faculty of Computers and Automatic Control of Bucharest, Romania.

Professor Florin Gheorghe Filip, member of the Romanian Academy. Is the vice-president of the Romanian Academy and a senior researcher the National Computer Science Research and Development Institute, Bucharest, Romania.

Dan Stefanoiu is Professor at "Politehnica" University of Bucharest, Romania.
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