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Nonlinear Optimization in Electrical Engineering with Applications in MATLAB®

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IET Digital Library

This title is available electronically through the IET Digital Library

  • Author:

  • Year: 2013

  • Format: Hardback

  • Product Code: PBSP0080

  • ISBN: 978-1-84919-543-0

  • Pagination: 319 pp.

  • Stock Status: In stock

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Description

Nonlinear Optimization in Electrical Engineering with Applications in MATLAB® provides an introductory course on nonlinear optimization in electrical engineering, with a focus on applications including the design of electric, microwave and photonic circuits, wireless communications and digital filter design. Basic concepts are introduced using a step-by-step approach featuring a variety of practical electrical engineering-related examples and illustrated with MATLAB® codes that the reader can use and adapt.

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.

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, computer-aided design and modelling of microwave circuits, neural networks applications, smart analysis of microwave circuits and efficient optimization using time domain simulation methods.

Book readership

Nonlinear Optimization in Electrical Engineering with Applications in MATLAB® is essential reading for advanced students in electrical engineering and will also be of interest to electrical engineering professionals.

Book contents

1 Mathematical background

  • Introduction
  • Vectors
  • Matrices
  • The solution of linear systems of equations
  • Derivatives
  • Subspaces
  • Convergence rates
  • Functions and sets
  • Solutions of systems of nonlinear equations
  • Optimization problem definition

2 An introduction to linear programming

  • Introduction
  • Examples of linear programs
  • Standard form of an LP
  • Optimality conditions
  • The matrix form
  • Canonical augmented form
  • Moving from one basic feasible solution to another
  • Cost reduction
  • The classical Simplex method
  • Starting the Simplex method
  • Advanced topics

3 Classical optimization

  • Introduction
  • Single-variable Taylor expansion
  • Multidimensional Taylor expansion
  • Meaning of the gradient
  • Optimality conditions
  • Unconstrained optimization
  • Optimization with equality constraints
  • Lagrange multipliers
  • Optimization with inequality constraints
  • Optimization with mixed constraints

4 One-dimensional optimization-Line search

  • Introduction
  • Bracketing approaches
  • Derivative-free line search
  • Interpolation approaches
  • Derivative-based approaches
  • Inexact line search

5 Derivative-free unconstrained techniques

  • Why unconstrained optimization?
  • Classification of unconstrained optimization techniques
  • The random jump technique
  • The random walk method
  • Grid search method
  • The univariate method
  • The pattern search method
  • The Simplex method
  • Response surface approximation

6 First-order unconstrained optimization techniques

  • Introduction
  • The steepest descent method
  • The conjugate directions method
  • Conjugate gradient methods

7 Second-order unconstrained optimization techniques

  • Introduction
  • Newton’s method
  • The Levenberg–Marquardt method
  • Quasi-Newton methods

8 Constrained optimization techniques

  • Introduction
  • Problem definition
  • Possible optimization scenarios
  • A random search method
  • Finding a feasible starting point
  • The Complex method
  • Sequential linear programming
  • Method of feasible directions
  • Rosen’s projection method
  • Barrier and penalty methods

9 Introduction to global optimization techniques

  • Introduction
  • Statistical optimization
  • Nature-inspired global techniques

10 Adjoint sensitivity analysis

  • Introduction
  • Tellegen’s theorem
  • Adjoint network method
  • Adjoint sensitivity analysis of a linear system of equations
  • Time-domain adjoint sensitivity analysis

 

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