Part a (6 sessions): Dr. J. Brinkhuis (EUR);
Part b (6 sessions): Prof.dr.ir. C. Roos (TUD/RUL)
Course description:
Part a (Brinkhuis): Convex analysis and algorithms
This part consists of an introduction to the state of the art for convex optimization. Many examples and applications in finance and engineering will be given. Theory: Convex analysis, duality theory, Farkas' lemma, Karush-Kuhn-Tucker equations, cones, convex geometry, oracles. Methods: Line search, gradient methods, Newton method, conjugate gradient method, conic optimization, analysis of performance.
Literature: Lecture notes will be provided weekly. Prerequisites: None. Examination: Take home problems.
Part b (Roos): Interior-point methods
In this part we deal with some modelling techniques using linear and convex quadratic models, and with polynomial-time interior-point methods for solving the corresponding optimization problems. Models: Some examples (filter synthesis, synthesis of arrays of antennae) based on Tschebyshev approximation and its applications are given, as well as some recent applications in combinatorial optimization. Methods: The self-dual LO model, embedding of a general LO model in a self-dual model, polynomial-time solution method, including rounding to an exact solution, target-following methods, generalization to convex problems, smoothness condition (self-concordancy), analysis of Newton's method, specially structured problems.
Literature
1. Book: Theory and Algorithms for Linear Optimization: An Interior Point Approach,
by C. Roos, T. Terlaky and J.-Ph. Vial, Wiley, Chichester, 1997.
2. Lecture notes, provided when necessary. Prerequisites : None. Examination : Take home problems.
Addresses of the lecturers
Dr. J. Brinkhuis Prof.dr.ir. C. Roos
Econometric Institute Faculty of Information Technology and Systems
Erasmus University Rotterdam Delft University of Technology
P.O. Box 1738 Mekelweg 4
3000 DR Rotterdam 2628 CD Delft
Phone : 010 - 4081364 Phone : 015 - 2782530
E-mail : brinkhuis@wis.few.eur.nl E-mail : c.roos@its.tudelft.nl