Integer and Nonlinear Optimization
Kathrin Klamroth, Winter Term 2003/2004

Tuesday 12:15 - 13:45 in the large auditorium, and
Thursday 14:15 - 15:45 in the small auditorium, Bismarckstr.
Start of classes: 21.10.2003

Tutorials:
Tuesday 10:15 - 11:45, Übungsraum 1, Bismarckstr.
Thursday 10:15 - 11:45, seminar room, 12th floor, Martensstr. 3
Start of tutorials: 28.10.2003

Prerequisits: Linear Optimization

Literature:

G.L. Nemhauser and L.A. Wolsey:
"Integer and Combinatorial Optimization".
Wiley, 1988.

L.A. Wolsey:
"Integer Programming".
Wiley, 1998.

M.S. Bazaraa, H.D. Sherali and C.M. Shetty:
"Nonlinear Prorgramming: Theory and Algorithms".
Wiley, 1993.

J. Jahn:
"Introduction to the Theory of Nonlinear Optimization", 2nd. ed.
Springer, 1996.

Outline:

Part I: Integer Programming.
1. Introduction: Integer programs and their applications
2. Interrelations to Linear Programming
3. Polyhedral theory: Integer polyhedra and the theory of valid inequalities
4. Solution methods: Cutting plane algorithms, Branch and Bound, relaxation approaches, dynamic programming,...

Part II: Nonlinear Programming.
5. Introduction: Nonlinear programs and their applications
6. Convexity: Repetition of basic properties of convex sets and convex functions
7. Optimality conditions
8. Unconstrained optimization: Line search and multidimensional search methods
9. Constrained optimization: Penalty and barrier function methods, methods of feasible directions

Homework and course material:

ps-files: pdf-files:
Handout 1 (in the first tutorial): handout1.ps handout1.pdf
Exercise sheet 2 (23.10.03): homework2.ps homework2.pdf
Exercise sheet 3 (30.10.03): homework3.ps homework3.pdf
Exercise sheet 4 (06.11.03): homework4.ps homework4.pdf
Exercise sheet 5 (13.11.03): homework5.ps homework5.pdf
(Abgabe bis Donnerstag, 20.11.03, 14:00
im Numerik-Postkasten, Schlauch, MI)
Exercise sheet 6 (20.11.03): homework6.ps homework6.pdf
Exercise sheet 7 (27.11.03): homework7.ps homework7.pdf
Exercise sheet 8 (04.12.03): homework8.ps homework8.pdf
Exercise sheet 9 (11.12.03): homework9.ps homework9.pdf
Exercise sheet 10 (18.12.03): homework10.ps homework10.pdf
Exercise sheet 11 (08.01.04): homework11.ps homework11.pdf
Exercise sheet 12 (15.01.04): homework12.ps homework12.pdf
Exercise sheet 13 (22.01.04): homework13.ps homework13.pdf
Exercise sheet 14 (28.01.04): homework14.ps homework14.pdf

Questions!? Mail to: klamroth@am.uni-erlangen.de

Last Update: January 28, 2004 - Kathrin Klamroth - klamroth@am.uni-erlangen.de