GEORGE MASON UNIVERSITY
Department of Operations Research & Engineering and Mathematics
OR 741/MATH 689/CSI 741 - ADVANCED TOPICS
IN LINEAR PROGRAMMING, FALL 2000
Prerequisites: OR 541 and 641 or permission of instructor.
Monday, 4:30pm - 7:10pm; Science & Tech. II, Room 111
Professor Roman A. Polyak
Science and Technology II, Room 127; (703) 993-1685; fax: (703) 993-1521
Office Hours: Tuesday 3:00 - 5:00 pm or by appointment; email: email@example.com
Text: Chu-Cherng Fang and Sarat Puthenpura,
Optimization and Extensions (Theory and Algorithms), Prentice
Hall NJ, 1993
S. Wright, Primal - Dual Interior Point Methods, SIAM 1997
In this course, we will cover few classical LP topics, including Simplex-Method, Duality and Decomposition. Our main concentration, however, will be on recent developments in the IPM, including the original affine scaling method by I.I.Dikin (1967) and projective scaling algorithm by N.Karmarker (1984).
We will discuss the path-following central path and primal-dual IPM's, which are based on Classical Barrier and Distance functions. We will cover the basic results of the Modified Barrier Functions (MBF) theory for LP. Complexity issues, as well as numerical realizations, of the IPMs will be discussed.
We will have a computational project, which requires using CPLEX software.
25% homework; 30% midterm exam; 15% computational project
30% final exam (take home)
1. Linear programming, simplex
2. Duality, primal-dual systems, perturbation function and sensitivity.
3. Decomposition in LP.
4. Complexity in LP, Ellipsoid method - first LP method with polynomial complexity.
5. Affine scaling method. Rate of convergence.
6. Projective scaling methods.
7. Log - Barrier Function and path - following methods.
8. Distance function and central - path methods.
9. Primal - Dual IPM.
10. Complexity of the Primal - Dual IPM.
11. MBF in LP: basic properties, MBF method, convergence, rate of convergence.
FINAL December 18, 2000