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SYEN 3312 Optimization Methods in Systems Engineering, Spring 2010
Instructor
Dr. Nidhal Bouaynaya
Email address: nxbouaynaya@ualr.edu
Office: ETAS 300H
Office hours: T-R 2:00 pm - 4:00 pm or by appointment
Course information
Syllabus
Annoucements
- Office hours begin on Tuesday, Jan. 12, 2010.
- Homework # 1 is due on Jan. 26, 2010.
- Homework # 2 is postponed to Feb. 16, 2010, due to inclement weather.
- Homework # 3 is due on Feb. 23, 2010.
- Midterm I is scheduled on Tuesday March. 2, 2010.
- The review session for Midterm I is scheduled for Tuesday Feb. 23, 2010 from 12:00-1:00 pm in ETAS 280.
- Homework # 4 is due on March 9, 2010.
- Homework # 5 is due on April 1, 2010.
- Midterm II is scheduled on Thursday April 15, 2010.
- The review session for Midterm II is scheduled for Tuesday April 13.
Lecture Notes (password protected)
The below lecture notes span over several classes.
Homework Schedule
| Lecture |
Date |
Topic |
Chapter |
Homework Assigned |
| 1 |
1/12 |
Introduction. Examples. Math preliminary: Notation, real vector spaces, linear independence, matrices. |
1,2 |
|
| 2 |
1/14 |
Math preliminary: Inner product, norm. Eigenvalues and eigenvectors, quadratic forms, calculus of several variables, chain rule, Taylor series, gradient, level sets, directional derivative. |
3,5 |
|
| 3 |
1/19 |
Math preliminary review (continued). |
3,5 |
1.5, 2.7, 3.6, 3.17a. |
| 4 |
1/21 |
MATLAB review session |
|
|
| 5 |
1/26 |
Basics of unconstrained optimization: FONC |
6 |
|
| 6 |
1/28 |
Basics of unconstrained optimization: SONC |
6 |
|
| 7 |
2/2 |
Basics of unconstrained optimization: SOSC |
6 |
5.5, 5.8, 5.9, 6.2 |
| 8 |
2/4 & 2/9 |
Canceled due to inclement weather |
|
|
| 9 |
2/11 |
Basics of unconstrained optimization: SOSC |
6 |
|
| 10 |
2/16 |
One-dimensional search methods: Gloden Section search |
7 |
6.7, 6.8, 6.11, 6.18, 6.21. |
| 11 |
2/18 |
One-dimensional search methods: Newton Method |
7 |
|
| 12 |
2/23 |
- One-dimensional search methods: Secant Method
- Gradient Methods |
7, 8 |
7.2 (a,b), 7.3 (a,b), 7.10 |
| 13 |
2/25 |
- Midterm I |
|
|
| 14 |
03/02 |
- Multidimensional search methods: Gradient methods, steepest descent |
8 |
|
| 15 |
03/04 |
- Analysis of gradient methods, Multidimensional Newton's method |
8,9 |
|
| 16 |
03/09 |
- Analysis of Multidimensional Newton's method
Introduction to constrained optimization and linear programming |
15 |
|
| 17 |
03/11 |
Linear Programming: Examples and graphical solution |
15 |
|
| 18 |
03/16 |
- Linear Programming: Standard form
- Intro. to the Simplex method |
15, 16 |
15.1, 15.5, 15.10, 15.11 |
|
|
Spring break |
|
|
| 19 |
03/29 |
The Simplex method |
16 |
|
| 20 |
04/01 |
The two-phase simplex algorithm |
16 |
|
| 21 |
04/06 |
Problem solving session: formulation and solutions of LP problems |
16 |
|
| 22 |
04/13 |
Review session for Midterm II |
|
|
| 23 |
04/15 |
Midterm II |
|
|
| 24 |
04/20 |
Duality theory - Dual LP problems |
17 |
|
| 25 |
04/22 |
General Constrained Problems: Non-linear optimization |
19 |
|
| 26 |
04/27 |
programming session using MATLAB's optimization toolbox |
|
|
| 27 |
04/29 |
General Lagrange theorem |
19 |
|
| 28 |
05/04 |
General Lagrange theorem: Examples |
19 |
19.1 |
Quizzes
Exams
Class Blog
Useful links
Linear Programming Graphic Tutorial
A graphical representation of a 2D LP problem
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