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Optimization in Engineering Sciences : Exact Methods.
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 an...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Otros Autores: | , , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Hoboken :
Wiley,
2013.
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| Colección: | ISTE.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 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 problemChapter 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 problem3.2. 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 problem4.3. 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.