Nonlinear Optimization for Electrical
Engineers
Instructor: Mohamed Bakr
Date |
Lecture |
Description |
0 |
Course Outline |
|
Sept. 18th |
Introduction: Historical Background,
statement of optimization problem |
|
|
2 |
Introduction: Classifications of Optimization problems, Mathematical background |
Sept. 25th |
Classical Optimization Methods: single variable optimization, unconstrained multivariate optimization
|
|
|
4 |
Equality Constraints: Solution by Direct substitution, Method of constrained variation |
|
5 |
Equality Constriants: Method of Lagrange
multipliers |
Oct. 2nd |
Inequality constraints: Kuhn-Tucker Conditions, Constraint
qualification |
|
|
7 |
One Dimensional Search: why one dimensional search?, Search with Fixed Step
Size, Search with Accelerated Step size |
|
8 |
One Dimensional Search: Interval halving Method, Fibonacci Method,
Golden Section Search |
Oct. 16th |
One Dimensional Search: Interpolation Methods, |
|
|
10 |
One Dimensional Search: Quasi-Newton Method, Secant Method, Practical Consideration |
Oct. 23rd |
Unconstrained Nonlinear
Optimization: Introduction and basic
concepts |
|
|
12 |
Direct Search Methods: Random Walks, Grid Search, Univariate Method |
13 |
Conjugate Gradient
Methods: Hooke and Jeeves Method, Powell’s Method, Simplex Method |
|
Oct 30th |
Indirect Methods: Steepest Descent, Conjugate Directions, Conjugate Gradients |
|
|
15 |
2nd Order Methods: |
16 |
2nd Order Methods
(Cont’d): Quasi Newton Methods, The DFP formula, the BFGS formula, summary |
|
|
17 |
2nd Order Methods
(Cont’d): Linear Least Squares, Nonlinear Least
Squares, Newton-Gauss method, applications |
20 |
Constrained Nonlinear
Optimization: Introduction, Random Methods, Complex Method |
|
|
19 |
Some Constrained Optimization
Methods: Zoutendijk’s method of feasible directions |
|
20 |
Constrained Optimization
(Cont’d): Rosen’s
Gradient projection Method |
21 |
Constrained Optimization
(Cont’d): Quadratic
Programming |
|
|
22 |
Constrained Optimization
(Cont’d): Sequential
Quadratic Programming |
|
23 |
Constrained Optimization
(Cont’d):
Penalty and Barrier Methods |
24 |
Global Optimization Techniques:
Genetic
Algorithms |
|
|
25 |
Global Optimization Techniques
(Cont’d): Simulated annealing |
|
26 |
Global Optimization
Techniques(Cont’d): Particle Swarm Optimization |
|
27 |
Linear Programming: The Simplex Method |
|
28 |
Linear Programming: Interior Point Methods |
|
29 |
Space Mapping Optimization and
Modeling: Basic
Concepts, classical Space Mapping, Aggressive Space Mapping |
|
30 |
Space Mapping (Cont’d): surrogate-based optimization,
Output Space Mapping |
|
31 |
Adjoint Variable Methods: The Dynamic Case |