IE 309: Optimization of
Large-Scale Linear Systems
Instructor:
Nick Sahinidis (nikos@uiuc.edu)
Course Objectives:
Offer a thorough coverage of Linear Programming.
Topics covered:
- Fundamentals: Linear Algebra,
Polyhedral Theory, Duality
- Algorithms: Simplex, interior
point methods, decomposition, subgradient optimization
- Numerical stability and other
implementation issues
- Software: OSL, CPLEX, MINOS,
GAMS.
Text:
There are no required texts for this course. Recommended readings are:
- Linear Programming and
Extensions by Dantzig.
- Linear Programming and
Network Flows by Bazaraa, Jarvis and Sherali.
- Linear Optimization and
Extensions. Theory and Algorithms by Fang and Puthenpura.
Extensive additional material from research papers will be
provided in class.
A General Bibliography on Optimization is available here
Credit:
3 hours or 3/4 or 1 unit. Course grade will be based on homework (33.3%) and
two take home exams (33.3% each). Those taking the course for 1 unit will be
required to complete a computational project accounting for 25% of their grade.
Course Contents:
- Linear Programming Models
- Linear Algebra and Polyhedral
Theory
- Fundamental Properties of
Linear Programs
- The Simplex Method
- Numerically Stable forms and
other Implementation Issues
- Duality and Postoptimality
Analysis
- Column Generation and Benders
Decomposition
- Stochastic Linear Programming
- Lagrangian Relaxation Methods
- Projective Scaling, Primal
and Dual Affine Scaling Methods
- Semidefinite Programming
- Use of computer software and
implementation of algorithms
Detailed Course Schedule
To Sigma Optimization Teaching
Activities