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About this book

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.

Table of Contents

Chapter 1. Introducing MATLAB and the MATLAB Working Environment

Abstract
MATLAB is a platform for scientific calculation and high-level programming which uses an interactive environment that allows you to conduct complex calculation tasks more efficiently than with traditional languages, such as C, C++ and FORTRAN. It is the one of the most popular platforms currently used in the sciences and engineering.
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Chapter 2. MATLAB Programming

Abstract
MATLAB can be used as a high-level programming language including data structures, functions, instructions for flow control, management of inputs/outputs and even object-oriented programming.
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Chapter 3. Basic MATLAB Functions for Linear and Non-Linear Optimization

Abstract
MATLAB allows you to solve equations and systems of equations using the commands below:
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Chapter 4. Optimization by Numerical Methods: Solving Equations

Abstract
MATLAB is able to implement a number of algorithms which provide numerical solutions to certain problems which play a central role in the solution of non-linear equations. Such algorithms are easy to construct in MATLAB and are stored as M-files. From previous chapters we know that an M-file is simply a sequence of MATLAB commands or functions that accept arguments and produces output. The M-files are created using the text editor.
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Chapter 5. Optimization Using Symbolic Computation

Abstract
The following commands can be used for the solution of symbolic equations and systems of equations:
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Chapter 6. Optimization Techniques Via The Optimization Toolbox

Abstract
The Optimization Toolbox provides algorithms for solving a wide range of optimization problems. It contains routines that put into practice the most widely used methods for minimization and maximization.
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Chapter 7. Differentiation in one and Several Variables. Applications to Optimization

Abstract
The derivative of a real function at a point is the instantaneous rate of change of that function in a neighborhood of the point; i.e., it is a measure of how the dependent variable changes as a result of a small change in the independent variable.
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Chapter 8. Optimization of Functions of Complex Variables

Abstract
MATLAB implements a simple way to work with complex numbers in binary form a+bi or a+bj, representing the imaginary unit by means of the symbol i or j. Note that it is not necessary to include the product symbol (asterisk) before the imaginary unit, but if it is included, everything still works correctly. It is important, however, that spaces are not introduced between the imaginary unit i and its coefficient.
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Chapter 9. Algebraic Expressions, Polynomials, Equations and Systems. Tools for Optimization

Abstract
MATLAB incorporates a wide range of commands, including simplification, expansion and factorization, that allow you to work with algebraic expressions. The following table shows the most common commands used when working with algebraic expressions.
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