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 include classical optimization methods, one dimensional optimization, unconstrained optimization, constrained optimization, global optimization, space mapping optimization, and adjoint variable methods.
* Basic concepts are introduced using a step-by-step approach
* Features a variety of practical electrical engineering-related examples
* Illustrated with MATLAB® codes that the reader can use and adapt.
* Topics covered include: classical optimization methods, one dimensional optimization, unconstrained optimization, constrained optimization, global optimization, space mapping optimization and adjoint variable methods.
It will be essential reading for advanced students in electrical engineering and will also interest electrical engineering professionals.
Author(s): Mohamed Bakr
Publisher: The Institution of Engineering and Technology
Year: 2013
Language: English
Pages: 308
Tags: Библиотека;Компьютерная литература;Matlab / Simulink;
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
