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作者 Borne, Pierre
書名 Optimization in Engineering Sciences : Exact Methods
出版項 Somerset : John Wiley & Sons, Incorporated, 2012
©2013
國際標準書號 9781118577844 (electronic bk.)
9781848214323
book jacket
版本 1st ed
說明 1 online resource (328 pages)
text txt rdacontent
computer c rdamedia
online resource cr rdacarrier
系列 Iste
Iste
附註 Intro -- Title Page -- Contents -- Foreword -- Preface -- List of Acronyms -- Chapter 1. Linear Programming -- 1.1. Objective of linear programming -- 1.2. Stating the problem -- 1.3. Lagrange method -- 1.4. Simplex algorithm -- 1.4.1. Principle -- 1.4.2. Simplicial form formulation -- 1.4.3. Transition from one simplicial form to another -- 1.4.4. Summary of the simplex algorithm -- 1.5. Implementation example -- 1.6. Linear programming applied to the optimization of resource allocation -- 1.6.1. Areas of application -- 1.6.2. Resource allocation for advertising -- 1.6.3. Optimization of a cut of paper rolls -- 1.6.4. Structure of linear program of an optimal control problem -- Chapter 2. Nonlinear Programming -- 2.1. Problem formulation -- 2.2. Karush-Kuhn-Tucker conditions -- 2.3. General search algorithm -- 2.3.1. Main steps -- 2.3.2. Computing the search direction -- 2.3.3. Computation of advancement step -- 2.4. Monovariable methods -- 2.4.1. Coggin's method (of polynomial interpolation) -- 2.4.2. Golden section method -- 2.5. Multivariable methods -- 2.5.1. Direct search methods -- 2.5.2. Gradient methods -- Chapter 3. Dynamic Programming -- 3.1. Principle of dynamic programming -- 3.1.1. Stating the problem -- 3.1.2. Decision problem -- 3.2. Recurrence equation of optimality -- 3.3. Particular cases -- 3.3.1. Infinite horizon stationary problems -- 3.3.2. Variable horizon problem -- 3.3.3. Random horizon problem -- 3.3.4. Taking into account sum-like constraints -- 3.3.5. Random evolution law -- 3.3.6. Initialization when the final state is imposed -- 3.3.7. The case when the necessary information is not always available -- 3.4. Examples -- 3.4.1. Route optimization -- 3.4.2. The smuggler problem -- Chapter 4. Hopfield Networks -- 4.1. Structure -- 4.2. Continuous dynamic Hopfield networks -- 4.2.1. General problem
4.2.2. Application to the traveling salesman problem -- 4.3. Optimization by Hopfield networks, based on simulated annealing -- 4.3.1. Deterministic method -- 4.3.2. Stochastic method -- Chapter 5. Optimization in System Identification -- 5.1. The optimal identification principle -- 5.2. Formulation of optimal identification problems -- 5.2.1. General problem -- 5.2.2. Formulation based on optimization theory -- 5.2.3. Formulation based on estimation theory (statistics) -- 5.3. Usual identification models -- 5.3.1. General model -- 5.3.2. Rational input/output (RIO) models -- 5.3.3. Class of autoregressive models (ARMAX) -- 5.3.4. Class of state space representation models -- 5.4. Basic least squares method -- 5.4.1. LSM type solution -- 5.4.2. Geometric interpretation of the LSM solution -- 5.4.3. Consistency of the LSM type solution -- 5.4.4. Example of application of the LSM for an ARX model -- 5.5. Modified least squares methods -- 5.5.1. Recovering lost consistency -- 5.5.2. Extended LSM -- 5.5.3. Instrumental variables method -- 5.6. Minimum prediction error method -- 5.6.1. Basic principle and algorithm -- 5.6.2. Implementation of the MPEM for ARMAX models -- 5.6.3. Convergence and consistency of MPEM type estimations -- 5.7. Adaptive optimal identification methods -- 5.7.1. Accuracy/adaptability paradigm -- 5.7.2. Basic adaptive version of the LSM -- 5.7.3. Basic adaptive version of the IVM -- 5.7.4. Adaptive window versions of the LSM and IVM -- Chapter 6. Optimization of Dynamic Systems -- 6.1. Variational methods -- 6.1.1. Variation of a functional -- 6.1.2. Constraint-free minimization -- 6.1.3. Hamilton canonical equations -- 6.1.4. Second-order conditions -- 6.1.5. Minimization with constraints -- 6.2. Application to the optimal command of a continuous process, maximum principle -- 6.2.1. Formulation -- 6.2.2. Examples of implementation
6.3. Maximum principle, discrete case -- 6.4. Principle of optimal command based on quadratic criteria -- 6.5. Design of the LQ command -- 6.5.1. Finite horizon LQ command -- 6.5.2. The infinite horizon QL command -- 6.5.3. Robustness of the LQ command -- 6.6. Optimal filtering -- 6.6.1. Kalman-Bucy predictor -- 6.6.2. Kalman-Bucy filter -- 6.6.3. Stability of Kalman-Bucy estimators -- 6.6.4. Robustness of Kalman-Bucy estimators -- 6.7. Design of the LQG command -- 6.8. Optimization problems connected to quadratic linear criteria -- 6.8.1. Optimal control by state feedback -- 6.8.2. Quadratic stabilization -- 6.8.3. Optimal command based on output feedback -- Chapter 7. Optimization of Large-Scale Systems -- 7.1. Characteristics of complex optimization problems -- 7.2. Decomposition techniques -- 7.2.1. Problems with block-diagonal structure -- 7.2.2. Problems with separable criteria and constraints -- 7.3. Penalization techniques -- 7.3.1. External penalization technique -- 7.3.2. Internal penalization technique -- 7.3.3. Extended penalization technique -- Chapter 8. Optimization and Information Systems -- 8.1. Introduction -- 8.2. Factors influencing the construction of IT systems -- 8.3. Approaches -- 8.4. Selection of computing tools -- 8.5. Difficulties in implementation and use -- 8.6. Evaluation -- 8.7. Conclusions -- Bibliography -- Index
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
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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2020. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries
鏈接 Print version: Borne, Pierre Optimization in Engineering Sciences : Exact Methods Somerset : John Wiley & Sons, Incorporated,c2012 9781848214323
主題 Engineering mathematics
Electronic books
Alt Author Popescu, Dumitru
Stefanoiu, Dan
Filip, Florin Gheorghe
Filip, Florin Gh
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