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MATLAB optimization techniques
Perez Lopez, Cesar.
اطلاعات کتابشناختی
MATLAB optimization techniques
Author :
Perez Lopez, Cesar.
Publisher :
Apress,
Pub. Year :
2014
Subjects :
Mathematical optimization -- Computer programs. Numerical analysis -- Data processing.
Call Number :
QA 402 .5 .P47 2014
جستجو در محتوا
ترتيب
شماره صفحه
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فهرست مطالب
Contents at a Glance
(3)
Contents
(279)
About the Author
(283)
Chapter 1: Introducing MATLAB and the MATLAB Working Environment
(4)
1.1 Introduction
(4)
1.1.1 Developing Algorithms and Applications
(5)
1.1.2 Data Access and Analysis
(8)
1.1.3 Data Visualization
(9)
1.1.4 Numerical Calculation
(12)
1.1.5 Publication of Results and Distribution of Applications
(13)
1.2 The MATLAB Working Environment
(14)
1.3 Help in MATLAB
(19)
Chapter 2: MATLAB Programming
(25)
2.1 MATLAB Programming
(25)
2.1.1 The Text Editor
(25)
2.1.2 Scripts
(28)
2.1.3 Functions and M-files. Eval and Feval
(31)
2.1.4 Local and Global Variables
(34)
2.1.5 Data Types
(36)
2.1.6 Flow Control: FOR, WHILE and IF ELSEIF Loops
(37)
FOR Loops
(37)
WHILE Loops
(38)
IF ELSEIF ELSE END Loops
(39)
SWITCH and CASE
(41)
CONTINUE
(42)
BREAK
(42)
TRY... CATCH
(44)
RETURN
(44)
2.1.7 Subfunctions
(45)
2.1.8 Commands in M-files
(46)
2.1.9 Functions Relating to Arrays of Cells
(47)
2.1.10 Multidimensional Array Functions
(50)
Chapter 3: Basic MATLAB Functions for Linear and Non-Linear Optimization
(54)
3.1 Solutions of Equations and Systems of Equations
(54)
3.2 Working with Polynomials
(60)
Chapter 4: Optimization by Numerical Methods: Solving Equations
(68)
4.1 Non-Linear Equations
(68)
4.1.1 The Fixed Point Method for Solving x = g(x)
(68)
4.1.2 Newton’s Method for Solving the Equation f(x) = 0
(71)
4.1.3 Schröder’s Method for Solving the Equation f(x) = 0
(73)
4.2 Systems of Non-Linear Equations
(73)
4.2.1 The Seidel Method
(74)
4.2.2 The Newton-Raphson Method
(74)
Chapter 5: Optimization Using Symbolic Computation
(82)
5.1 Symbolic Equations and Systems of Equations
(82)
Chapter 6: Optimization Techniques Via The Optimization Toolbox
(86)
6.1 The Optimization Toolbox
(86)
6.1.1 Standard Algorithms
(86)
6.1.2 Large Scale Algorithms
(86)
6.2 Minimization Algorithms
(87)
6.2.1 Multiobjective Problems
(87)
6.2.2 Non-Linear Scalar Minimization With Boundary Conditions
(90)
6.2.3 Non-Linear Minimization with Restrictions
(90)
6.2.4 Minimax Optimization: fminimax and fminuc
(92)
6.2.5 Minimax Optimization
(93)
6.2.6 Minimum Optimization: fminsearch and fminuc
(94)
6.2.7 Semi-Infinitely Constrained Minimization
(94)
6.2.8 Linear Programming
(95)
6.2.9 Quadratic programming
(97)
6.3 Equation Solving Algorithms
(99)
6.3.1 Solving Equations and Systems of Equations
(99)
6.4 Fitting Curves by Least Squares
(101)
6.4.1 Conditional Least Squares Problems
(101)
6.4.2 Non- Linear Least Squares Problems
(101)
6.4.3 Linear Non- Negative Least Squares Problems
(102)
Chapter 7: Differentiation in one and Several Variables. Applications to Optimization
(110)
7.1 Derivatives
(110)
7.2 Par tial Derivatives
(112)
7.3 Applications of Derivatives. Tangents, Asymptotes, Extreme Points and Turning Points
(114)
7.4 Differentiation of Functions of Several Variables
(118)
7.5 Maxima and Minima of Functions of Several Variables
(123)
7.6 Conditional Minima and Maxima. The Method of “Lagrange Multipliers”
(131)
7.7 Vector Differential Calculus
(134)
7.8 The Composite Function Theorem
(135)
7.9 The Implicit Function Theorem
(136)
7.10 The Inverse Function Theorem
(137)
7.11 The Change of Variables Theorem
(139)
7.12 Series Expansions in Several Variables
(139)
7.13 Vector Fields. Curl, Divergence and the Laplacian
(140)
Spherical, Cylindrical and Rectangular Coordinates
(142)
Chapter 8: Optimization of Functions of Complex Variables
(165)
8.1 Complex Numbers
(165)
8.2 General Functions of a Complex Variable
(166)
8.2.1 Trigonometric Functions of a Complex Variable
(166)
8.2.2 Hyperbolic Functions of a Complex Variable
(167)
8.2.3 Exponential and Logarithmic Functions of a Complex Variable
(168)
8.3 Specific Functions of a Complex Variable
(169)
8.4 Basic Functions with Complex Vector Arguments
(170)
8.5 Basic Functions with Complex Matrix Arguments
(175)
8.6 General Functions with Complex Matrix Arguments
(181)
8.6.1 Trigonometric Functions of a Complex Matrix Variable
(181)
8.6.2 Hyperbolic Functions of a Complex Matrix Variable
(186)
8.6.3 Exponential and Logarithmic Functions of a Complex Matrix Variable
(190)
8.6.4 Specific Functions of a Complex Matrix Variable
(192)
8.7 Matrix Operations with Real and Complex Variables
(195)
Chapter 9: Algebraic Expressions, Polynomials, Equations and Systems. Tools for Optimization
(216)
9.1 Expanding, Simplifying and Factoring Algebraic Expressions
(216)
9.2 Polynomials
(219)
9.3 Polynomial Interpolation
(223)
9.4 Solving Equations and Systems of Equations
(231)
9.4.1 General Methods
(231)
9.4.2 The Biconjugate Gradient Method
(233)
9.4.3 The Conjugate Gradients Method
(236)
9.4.4 The Residual Method
(238)
9.4.5 The Symmetric and Non-Negative Least Squares Method
(241)
9.5 Solving Linear Systems of Equations
(243)