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Optimization in Engineering Sciences


Optimization in Engineering Sciences

Exact Methods
11. Aufl.

von: Pierre Borne, Dumitru Popescu, Florin Gheorghe Filip, Dan Stefanoiu

140,99 €

Verlag: Wiley
Format: EPUB
Veröffentl.: 24.01.2013
ISBN/EAN: 9781118577844
Sprache: englisch
Anzahl Seiten: 336

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Beschreibungen

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

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