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