Nonlinear Optimization in Electrical Engineering with Applications in MATLAB
Author: Mohamed Bakr
Copyright: 2013
Binding: Hardcover
Pages: 319
ISBN: 9781849195430
List Price: $72.00
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DESCRIPTION
This textbook offers a smooth introduction to nonlinear optimization for undergraduate and graduate level electrical and computer engineering students. It is based on Dr. Bakr's highly successful optimization course taught at the University of Waterloo in concert with Research in Motion (RIM). While several nonlinear optimization books exist for students, they are focused toward math and physics. This textbook provides the basic concepts and fundamentals, and then tightly focuses on electrical engineering applications with extensive examples, illustrations, and MATLAB® code development. There is less focus on lengthy mathematical derivations and more on practical applications.
Topics covered in Nonlinear Optimization in Electrical Engineering with Applications in MATLAB® classical optimization methods, one dimensional optimization, unconstrained optimization, constrained optimization, global optimization, space mapping optimization, and adjoint variable methods.
TABLE OF CONTENTS
1. Mathematical Background
1.1 Introduction
1.2 Vectors
1.3 Matrices
1.4 The solution of linear systems of equations
1.5 Derivatives
1.6 Subspaces
1.7 Convergence rates
1.8 Functions and sets
1.9 Solutions of systems of nonlinear equations
1.10 Optimization problem definition
References
Problems
2 An introduction to linear programming
2.1 Introduction
2.2 Examples of linear programs
2.3 Standard form of an LP
2.4 Optimality conditions
2.5 The matrix form
2.6 Canonical augmented form
2.7 Moving from one basic feasible solution to another
2.8 Cost reduction
2.9 The classical Simplex method
2.10 Starting the Simplex method
2.11 Advanced topics
References
Problems
3 Classical optimization
3.1 Introduction
3.2 Singlevariable Taylor expansion
3.3 Multidimensional Taylor expansion
3.4 Meaning of the gradient
3.5 Optimality conditions
3.6 Unconstrained optimization
3.7 Optimization with equality constraints
3.8 Lagrange multipliers
3.9 Optimization with inequality constraints
3.10 Optimization with mixed constraints
A3.1 Quadratic programming
A3.2 Sequential quadratic programming
References
Problems
4 Onedimensional optimizationLine search
4.1 Introduction
4.2 Bracketing approaches
4.3 Derivativefree line search
4.4 Interpolation approaches
4.5 Derivativebased approaches
4.6 Inexact line search
A4.1 Tuning of electric circuits
References
Problems
5 Derivativefree unconstrained techniques
5.1 Why unconstrained optimization?
5.2 Classification of unconstrained optimization techniques
5.3 The random jump technique
5.4 The random walk method
5.5 Grid search method
5.6 The univariate method
5.7 The pattern search method
5.8 The Simplex method
5.9 Response surface approximation
A5.1 Electrical application: impedance transformers
A5.2 Electrical application: the design of photonic devices
References
Problems
6 Firstorder unconstrained optimization techniques
6.1 Introduction
6.2 The steepest descent method
6.3 The conjugate directions method
6.4 Conjugate gradient methods
A6.1 Solution of large systems of linear equations
A6.2 The design of digital FIR filters
References
Problems
7 Secondorder unconstrained optimization techniques
7.1 Introduction
7.2 Newton’s method
7.3 The Levenberg–Marquardt method
7.4 QuasiNewton methods
A7.1 Wireless channel characterization
A7.2 The parameter extraction problem
A7.3 Artificial neural networks training
References
Problems
8 Constrained optimization techniques
8.1 Introduction
8.2 Problem definition
8.3 Possible optimization scenarios
8.4 A random search method
8.5 Finding a feasible starting point
8.6 The Complex method
8.7 Sequential linear programming
8.8 Method of feasible directions
8.9 Rosen’s projection method
8.10 Barrier and penalty methods
A8.1 Electrical engineering application: analog filter design
A8.2 Spectroscopy
References
Problems
9 Introduction to global optimization techniques
9.1 Introduction
9.2 Statistical optimization
9.3 Natureinspired global techniques
A9.1 Least pth optimization of filters
A9.2 Pattern recognition
References
Problems
10 Adjoint sensitivity analysis
10.1 Introduction
10.2 Tellegen’s theorem
10.3 Adjoint network method
10.4 Adjoint sensitivity analysis of a linear system of equations
10.5 Timedomain adjoint sensitivity analysis
A10.1 Sensitivity analysis of highfrequency structures
References
Problems
Index
ABOUT THE AUTHOR
Mohamed Bakr is an Associate Professor at the Department of Electrical and Computer Engineering, McMaster University, Canada, where his research interests include optimization methods, computeraided design and modelling of microwave circuits, neural networks applications, smart analysis of microwave circuits and efficient optimization using time domain simulation methods.
