Lopez MATLAB Optimization Techniques

1. Auflage 2014
ISBN: 978-1-4842-0292-0
Verlag: APRESS
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 284 Seiten, eBook

MATLAB is a high-level language and environment for numerical computation, visualization, and programming. Using MATLAB, you can analyze data, develop algorithms, and create models and applications. The language, tools, and built-in math functions enable you to explore multiple approaches and reach a solution faster than with spreadsheets or traditional programming languages, such as C/C++ or Java. MATLAB Optimization Techniques introduces you to the MATLAB language with practical hands-on instructions and results, allowing you to quickly achieve your goals. It begins by introducing the MATLAB environment and the structure of MATLAB programming before moving on to the mathematics of optimization. The central part of the book is dedicated to MATLAB’s Optimization Toolbox, which implements state-of-the-art algorithms for solving multiobjective problems, non-linear minimization with boundary conditions and restrictions, minimax optimization, semi-infinitely constrained minimization and linear and quadratic programming. A wide range of exercises and examples are included, illustrating the most widely used optimization methods.

Zielgruppe

Popular/general

Autoren/Hrsg.

Lopez, Cesar

Inhaltsverzeichnis

1;Contents at a Glance;3
2;Contents;279
3;About the Author;283
4;Chapter 1: Introducing MATLAB and the MATLAB Working Environment;4
4.1;1.1 Introduction;4
4.1.1;1.1.1 Developing Algorithms and Applications;5
4.1.2;1.1.2 Data Access and Analysis;8
4.1.3;1.1.3 Data Visualization;9
4.1.4;1.1.4 Numerical Calculation;12
4.1.5;1.1.5 Publication of Results and Distribution of Applications;13
4.2;1.2 The MATLAB Working Environment;14
4.3;1.3 Help in MATLAB;19
5;Chapter 2: MATLAB Programming;25
5.1;2.1 MATLAB Programming;25
5.1.1;2.1.1 The Text Editor;25
5.1.2;2.1.2 Scripts;28
5.1.3;2.1.3 Functions and M-files. Eval and Feval;31
5.1.4;2.1.4 Local and Global Variables;34
5.1.5;2.1.5 Data Types;36
5.1.6;2.1.6 Flow Control: FOR, WHILE and IF ELSEIF Loops;37
5.1.6.1;FOR Loops;37
5.1.6.2;WHILE Loops;38
5.1.6.3;IF ELSEIF ELSE END Loops;39
5.1.6.4;SWITCH and CASE;41
5.1.6.5;CONTINUE;42
5.1.6.6;BREAK;42
5.1.6.7;TRY... CATCH;44
5.1.6.8;RETURN;44
5.1.7;2.1.7 Subfunctions;45
5.1.8;2.1.8 Commands in M-files;46
5.1.9;2.1.9 Functions Relating to Arrays of Cells;47
5.1.10;2.1.10 Multidimensional Array Functions;50
6;Chapter 3: Basic MATLAB Functions for Linear and Non-Linear Optimization;54
6.1;3.1 Solutions of Equations and Systems of Equations;54
6.2;3.2 Working with Polynomials;60
7;Chapter 4: Optimization by Numerical Methods: Solving Equations;68
7.1;4.1 Non-Linear Equations;68
7.1.1;4.1.1 The Fixed Point Method for Solving x = g(x);68
7.1.2;4.1.2 Newton’s Method for Solving the Equation f(x) = 0;71
7.1.3;4.1.3 Schröder’s Method for Solving the Equation f(x) = 0;73
7.2;4.2 Systems of Non-Linear Equations;73
7.2.1;4.2.1 The Seidel Method;74
7.2.2;4.2.2 The Newton-Raphson Method;74
8;Chapter 5: Optimization Using Symbolic Computation;82
8.1;5.1 Symbolic Equations and Systems of Equations;82
9;Chapter 6: Optimization Techniques Via The Optimization Toolbox;86
9.1;6.1 The Optimization Toolbox;86
9.1.1;6.1.1 Standard Algorithms;86
9.1.2;6.1.2 Large Scale Algorithms;86
9.2;6.2 Minimization Algorithms;87
9.2.1;6.2.1 Multiobjective Problems;87
9.2.2;6.2.2 Non-Linear Scalar Minimization With Boundary Conditions;90
9.2.3;6.2.3 Non-Linear Minimization with Restrictions;90
9.2.4;6.2.4 Minimax Optimization: fminimax and fminuc;92
9.2.5;6.2.5 Minimax Optimization;93
9.2.6;6.2.6 Minimum Optimization: fminsearch and fminuc;94
9.2.7;6.2.7 Semi-Infinitely Constrained Minimization;94
9.2.8;6.2.8 Linear Programming;95
9.2.9;6.2.9 Quadratic programming;97
9.3;6.3 Equation Solving Algorithms;99
9.3.1;6.3.1 Solving Equations and Systems of Equations;99
9.4;6.4 Fitting Curves by Least Squares;101
9.4.1;6.4.1 Conditional Least Squares Problems;101
9.4.2;6.4.2 Non- Linear Least Squares Problems;101
9.4.3;6.4.3 Linear Non- Negative Least Squares Problems;102
10;Chapter 7: Differentiation in one and Several Variables. Applications to Optimization;110
10.1;7.1 Derivatives;110
10.2;7.2 Par tial Derivatives;112
10.3;7.3 Applications of Derivatives. Tangents, Asymptotes, Extreme Points and Turning Points;114
10.4;7.4 Differentiation of Functions of Several Variables;118
10.5;7.5 Maxima and Minima of Functions of Several Variables;123
10.6;7.6 Conditional Minima and Maxima. The Method of “Lagrange Multipliers”;131
10.7;7.7 Vector Differential Calculus;134
10.8;7.8 The Composite Function Theorem;135
10.9;7.9 The Implicit Function Theorem;136
10.10;7.10 The Inverse Function Theorem;137
10.11;7.11 The Change of Variables Theorem;139
10.12;7.12 Series Expansions in Several Variables;139
10.13;7.13 Vector Fields. Curl, Divergence and the Laplacian;140
10.14;Spherical, Cylindrical and Rectangular Coordinates;142
11;Chapter 8: Optimization of Functions of Complex Variables;165
11.1;8.1 Complex Numbers;165
11.2;8.2 General Functions of a Complex Variable;166
11.2.1;8.2.1 Trigonometric Functions of a Complex Variable;166
11.2.2;8.2.2 Hyperbolic Functions of a Complex Variable;167
11.2.3;8.2.3 Exponential and Logarithmic Functions of a Complex Variable;168
11.3;8.3 Specific Functions of a Complex Variable;169
11.4;8.4 Basic Functions with Complex Vector Arguments;170
11.5;8.5 Basic Functions with Complex Matrix Arguments;175
11.6;8.6 General Functions with Complex Matrix Arguments;181
11.6.1;8.6.1 Trigonometric Functions of a Complex Matrix Variable;181
11.6.2;8.6.2 Hyperbolic Functions of a Complex Matrix Variable;186
11.6.3;8.6.3 Exponential and Logarithmic Functions of a Complex Matrix Variable;190
11.6.4;8.6.4 Specific Functions of a Complex Matrix Variable;192
11.7;8.7 Matrix Operations with Real and Complex Variables;195
12;Chapter 9: Algebraic Expressions, Polynomials, Equations and Systems. Tools for Optimization;216
12.1;9.1 Expanding, Simplifying and Factoring Algebraic Expressions;216
12.2;9.2 Polynomials;219
12.3;9.3 Polynomial Interpolation;223
12.4;9.4 Solving Equations and Systems of Equations;231
12.4.1;9.4.1 General Methods;231
12.4.2;9.4.2 The Biconjugate Gradient Method;233
12.4.3;9.4.3 The Conjugate Gradients Method;236
12.4.4;9.4.4 The Residual Method;238
12.4.5;9.4.5 The Symmetric and Non-Negative Least Squares Method;241
12.5;9.5 Solving Linear Systems of Equations;243

Über Autor(innen)

César Perez Lopez is a Professor at the Department of Statistics and Operations Research at the University of Madrid. César Perez Lopez is also a Mathematician and Economist at the National Statistics Institute (INE) in Madrid, a body which belongs to the Superior Systems and Information Technology Department of the Spanish Government. César also currently works at the Institute for Fiscal Studies in Madrid.