CENG 504
Optimization Methods
Unconstrained optimization; one-dimensional search, gradient search methods. Constrained optimization; linear and integer programming. Heuristics. Non-derivative methods (metaheuristics); simulated annealing, genetic algorithms, neural networks.
Class Hours
3 lecture hours
Prerequisite: Knowledge of calculus and elementary programming.
OBJECTIVE
To provide the fundamental concepts and mathematical tools in optimization theory.
LEARNING OUTCOMES
- Ability to formulate and solve engineering problems
- Ability to classify various optimization methods
- Ability to propose an optimization technique for a specific problem
- Ability to use optimization tools
TEXTBOOK
Chong, E. K. P., and Zak, S. H., An Introduction to Optimization, Fourth Edition, John Wiley & Sons, 2013.
Week | Topic |
1 | Introduction to optimization |
Math. Review | |
2 | Vector spaces and matrices, linear transformations, orthogonal projections |
3 | Quadratic forms, calculus, conditions for local minimizers |
Unconstrained optimization | |
4 | One dimensional search – golden section search, Fibonacci search |
5 | One dimensional search – Newton’s method |
6 | Multi-dimensional gradient methods – steepest descent, Newton’s method |
7 | Conjugate direction methods |
Constrained optimization | |
8 | Linear programming |
9 | Linear programming – simplex algorithm |
10
|
Integer programming |
11
|
Heuristics for optimization |
|
Non-derivative methods (Metaheuristics) |
12
|
Simulated annealing |
13
|
Genetic algorithms |
14
|
Artificial neural networks |
Instructor(s)
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