An introduction to optimization
"The purpose of the book is to give the reader a working knowledge of optimization theory and methods"--
| Otros Autores: | , |
|---|---|
| Formato: | Libro electrónico |
| Idioma: | Inglés |
| Publicado: |
Hoboken, New Jersey :
Wiley
2013.
|
| Edición: | 4th ed |
| Colección: | Wiley series in discrete mathematics and optimization.
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| Materias: | |
| Ver en Biblioteca Universitat Ramon Llull: | https://discovery.url.edu/permalink/34CSUC_URL/1im36ta/alma991009849088306719 |
Tabla de Contenidos:
- Cover; Half Title page; Title page; Copyright page; Dedication; Preface; Part I: Mathematical Review; Chapter 1: Methods of Proof and Some Notation; 1.1 Methods of Proof; 1.2 Notation; Exercises; Chapter 2: Vector Spaces and Matrices; 2.1 Vector and Matrix; 2.2 Rank of a Matrix; 2.3 Linear Equations; 2.4 Inner Products and Norms; Exercises; Chapter 3: Transformations; 3.1 Linear Transformations; 3.2 Eigenvalues and Eigenvectors; 3.3 Orthogonal Projections; 3.4 Quadratic Forms; 3.5 Matrix Norms; Exercises; Chapter 4: Concepts from Geometry; 4.1 Line Segments
- 4.2 Hyperplanes and Linear Varieties4.3 Convex Sets; 4.4 Neighborhoods; 4.5 Polytopes and Polyhedra; Exercises; Chapter 5: Elements of Calculus; 5.1 Sequences and Limits; 5.2 Differentiability; 5.3 The Derivative Matrix; 5.4 Differentiation Rules; 5.5 Level Sets and Gradients; 5.6 Taylor Series; Exercises; Part II: Unconstrained Optimization; Chapter 6: Basics of Set-Constrained and Unconstrained Optimization; 6.1 Introduction; 6.2 Conditions for Local Minimizers; Exercises; Chapter 7: One-Dimensional Search Methods; 7.1 Introduction; 7.2 Golden Section Search; 7.3 Fibonacci Method
- 7.4 Bisection Method7.5 Newton's Method; 7.6 Secant Method; 7.7 Bracketing; 7.8 Line Search in Multidimensional Optimization; Exercises; Chapter 8: Gradient Methods; 8.1 Introduction; 8.2 The Method of Steepest Descent; 8.3 Analysis of Gradient Methods; Exercises; Chapter 9: Newton's Method; 9.1 Introduction; 9.2 Analysis of Newton's Method; 9.3 Levenberg-Marquardt Modification; 9.4 Newton's Method for Nonlinear Least Squares; Exercises; Chapter 10: Conjugate Direction Methods; 10.1 Introduction; 10.2 The Conjugate Direction Algorithm; 10.3 The Conjugate Gradient Algorithm
- 10.4 The Conjugate Gradient Algorithm for Nonquadratic ProblemsExercises; Chapter 11: Quasi-Newton Methods; 11.1 Introduction; 11.2 Approximating the Inverse Hessian; 11.3 The Rank One Correction Formula; 11.4 The DFP Algorithm; 11.5 The BFGS Algorithm; Exercises; Chapter 12: Solving Linear Equations; 12.1 Least-Squares Analysis; 12.2 The Recursive Least-Squares Algorithm; 12.3 Solution to a Linear Equation with Minimum Norm; 12.4 Kaczmarz's Algorithm; 12.5 Solving Linear Equations in General; Exercises; Chapter 13: Unconstrained Optimization and Neural Networks; 13.1 Introduction
- 13.2 Single-Neuron Training13.3 The Backpropagation Algorithm; Exercises; Chapter 14: Global Search Algorithms; 14.1 Introduction; 14.2 The Nelder-Mead Simplex Algorithm; 14.3 Simulated Annealing; 14.4 Particle Swarm Optimization; 14.5 Genetic Algorithms; Exercises; Part III: Linear Programming; Chapter 15: Introduction to Linear Programming; 15.1 Brief History of Linear Programming; 15.2 Simple Examples of Linear Programs; 15.3 Two-Dimensional Linear Programs; 15.4 Convex Polyhedra and Linear Programming; 15.5 Standard Form Linear Programs; 15.6 Basic Solutions
- 15.7 Properties of Basic Solutions
