SE 521 Nonlinear Programming and Applications in
Industrial Engineering
Course Description
This course provides an advanced analytical and computational
approach to nonlinear optimization problems. The topics covered in this
course include: unconstrained optimization methods, constrained
optimization methods, convex analysis, Lagrangian relaxation,
nondifferentiable optimization, and applications in integer programming.
The course also provides a comprehensive treatment of optimality
conditions, Lagrange multiplier theory, and duality theory. Applications
are drawn from industrial engineering problems.
Prerequisite: Linear algebra and advanced calculus
Method of assessment
Exam 30 points
Homework assignments 20 points
Theoretical research 50 points
Schedule of topics
| Week |
Tasks |
| 1 |
Registration |
| 2 |
Introduction, Unconstrained Optimization -
Optimality Conditions |
| 3 |
Research proposal seminars |
| 4 |
Gradient Methods, Convergence Analysis of
Gradient Methods |
| 5 |
Newton And Gauss - Newton Methods |
| 6 |
Optimization Over A Convex Set; Optimality
Conditions, Research Progress |
| 7 |
Feasible Direction Methods |
| 8 |
Alternatives To Gradient Projection |
| 9 |
Constrained Optimization; Lagrange Multipliers,
Research Progress |
| 10 |
Constrained Optimization; Lagrange Multipliers |
| 11 |
Inequality Constraints |
| 12 |
Interior Point Methods, Research Progress |
| 13 |
Penalty Methods |
| 14 |
Augmented Lagrangian Methods |
| 15 |
Research Seminars |
References
- Nonlinear Programming by D.P. Bertsekas, Athena Scientific
- Nonlinear Programming: Theory and Algorithms by Bazaraa, Sherali,
and Shetty, Wiley & Sons
-
SE 305 Optimization Methods
|