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MATLAB Optimization Techniques

Book Description

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 MATLABs 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.

Table of Contents

  1. Cover
  2. Title
  3. Copyright
  4. Contents at a Glance
  5. Contents
  6. About the Author
  7. Chapter 1: Introducing MATLAB and the MATLAB Working Environment
    1. 1.1 Introduction
      1. 1.1.1 Developing Algorithms and Applications
      2. 1.1.2 Data Access and Analysis
      3. 1.1.3 Data Visualization
      4. 1.1.4 Numerical Calculation
      5. 1.1.5 Publication of Results and Distribution of Applications
    2. 1.2 The MATLAB Working Environment
    3. 1.3 Help in MATLAB
  8. Chapter 2: MATLAB Programming
    1. 2.1 MATLAB Programming
      1. 2.1.1 The Text Editor
      2. 2.1.2 Scripts
      3. 2.1.3 Functions and M-files. Eval and Feval
      4. 2.1.4 Local and Global Variables
      5. 2.1.5 Data Types
      6. 2.1.6 Flow Control: FOR, WHILE and IF ELSEIF Loops
      7. 2.1.7 Subfunctions
      8. 2.1.8 Commands in M-files
      9. 2.1.9 Functions Relating to Arrays of Cells
      10. 2.1.10 Multidimensional Array Functions
  9. Chapter 3: Basic MATLAB Functions for Linear and Non-Linear Optimization
    1. 3.1 Solutions of Equations and Systems of Equations
    2. 3.2 Working with Polynomials
  10. Chapter 4: Optimization by Numerical Methods: Solving Equations
    1. 4.1 Non-Linear Equations
      1. 4.1.1 The Fixed Point Method for Solving x = g(x)
      2. 4.1.2 Newton’s Method for Solving the Equation f(x) = 0
      3. 4.1.3 Schröder’s Method for Solving the Equation f(x) = 0
    2. 4.2 Systems of Non-Linear Equations
      1. 4.2.1 The Seidel Method
      2. 4.2.2 The Newton-Raphson Method
  11. Chapter 5: Optimization Using Symbolic Computation
    1. 5.1 Symbolic Equations and Systems of Equations
  12. Chapter 6: Optimization Techniques Via The Optimization Toolbox
    1. 6.1 The Optimization Toolbox
      1. 6.1.1 Standard Algorithms
      2. 6.1.2 Large Scale Algorithms
    2. 6.2 Minimization Algorithms
      1. 6.2.1 Multiobjective Problems
      2. 6.2.2 Non-Linear Scalar Minimization With Boundary Conditions
      3. 6.2.3 Non-Linear Minimization with Restrictions
      4. 6.2.4 Minimax Optimization: fminimax and fminuc
      5. 6.2.5 Minimax Optimization
      6. 6.2.6 Minimum Optimization: fminsearch and fminuc
      7. 6.2.7 Semi-Infinitely Constrained Minimization
      8. 6.2.8 Linear Programming
      9. 6.2.9 Quadratic programming
    3. 6.3 Equation Solving Algorithms
      1. 6.3.1 Solving Equations and Systems of Equations
    4. 6.4 Fitting Curves by Least Squares
      1. 6.4.1 Conditional Least Squares Problems
      2. 6.4.2 Non- Linear Least Squares Problems
      3. 6.4.3 Linear Non- Negative Least Squares Problems
  13. Chapter 7: Differentiation in one and Several Variables. Applications to Optimization
    1. 7.1 Derivatives
    2. 7.2 Par?tial Derivatives
    3. 7.3 Applications of Derivatives. Tangents, Asymptotes, Extreme Points and Turning Points
    4. 7.4 Differentiation of Functions of Several Variables
    5. 7.5 Maxima and Minima of Functions of Several Variables
    6. 7.6 Conditional Minima and Maxima. The Method of “Lagrange Multipliers”
    7. 7.7 Vector Differential Calculus
    8. 7.8 The Composite Function Theorem
    9. 7.9 The Implicit Function Theorem
    10. 7.10 The Inverse Function Theorem
    11. 7.11 The Change of Variables Theorem
    12. 7.12 Series Expansions in Several Variables
    13. 7.13 Vector Fields. Curl, Divergence and the Laplacian
    14. Spherical, Cylindrical and Rectangular Coordinates
  14. Chapter 8: Optimization of Functions of Complex Variables
    1. 8.1 Complex Numbers
    2. 8.2 General Functions of a Complex Variable
      1. 8.2.1 Trigonometric Functions of a Complex Variable
      2. 8.2.2 Hyperbolic Functions of a Complex Variable
      3. 8.2.3 Exponential and Logarithmic Functions of a Complex Variable
    3. 8.3 Specific Functions of a Complex Variable
    4. 8.4 Basic Functions with Complex Vector Arguments
    5. 8.5 Basic Functions with Complex Matrix Arguments
    6. 8.6 General Functions with Complex Matrix Arguments
      1. 8.6.1 Trigonometric Functions of a Complex Matrix Variable
      2. 8.6.2 Hyperbolic Functions of a Complex Matrix Variable
      3. 8.6.3 Exponential and Logarithmic Functions of a Complex Matrix Variable
      4. 8.6.4 Specific Functions of a Complex Matrix Variable
    7. 8.7 Matrix Operations with Real and Complex Variables
  15. Chapter 9: Algebraic Expressions, Polynomials, Equations and Systems. Tools for Optimization
    1. 9.1 Expanding, Simplifying and Factoring Algebraic Expressions
    2. 9.2 Polynomials
    3. 9.3 Polynomial Interpolation
    4. 9.4 Solving Equations and Systems of Equations
      1. 9.4.1 General Methods
      2. 9.4.2 The Biconjugate Gradient Method
      3. 9.4.3 The Conjugate Gradients Method
      4. 9.4.4 The Residual Method
      5. 9.4.5 The Symmetric and Non-Negative Least Squares Method
    5. 9.5 Solving Linear Systems of Equations