IE 401: Mathematical
Programming I
Instructor:
Nick
Sahinidis (nikos@uiuc.edu)
Course Objectives:
To offer an in depth study of the general theory and methods of Nonlinear
Programming. We will study modeling techniques, applications, algorithms,
software.
Text:
There are two required texts:
- Bazaraa, Sherali and Shetty:
Nonlinear Programming, Wiley, 2nd ed., 1993.
- Horst, Pardalos and Thoai:
Introduction to Global Optimization, Kluwer, 1995.
Extensive additional material from research papers will be
provided in class.
A General Bibliography on Optimization is available here
Credit:
1 unit. Course grade will be based on homework (30%), midterm (20%),
take-home final exam (20%), and computer project (30%).
Topics covered: (each lecture: two 50 minute
sessions)
- Introduction (1.5 lectures):
- Foundations (11 lectures):
- Convex/nonconvex sets
and functions
- Optimality conditions
- Concept of an
algorithm
- Classical Optimization
Methods (8 lectures):
- Line search
- Multidimensional
unconstrained optimization
- Penalty and Barrier
Methods
- Feasible directions
- Global Optimization Methods
(5 lectures):
- Lower bounding
- Branch and Bound
- Outer Approximation
- Decomposition
- Structured nonconvex
optimization problems
- Set
Covering/Packing/Partitioning
- Mixed-Integer
Nonlinear Programming
- Software (2.5 lectures)
To Sigma Optimization Teaching
Activities