Course CAO: Convex Analysis for Optimization

Time:	Monday 15.15 - 17.00 (September 12 - November 14)
Location:	From September 1, 2022, all LNMB courses can again be attended on the Campus Utrecht Science Park. Details about lecture rooms, as well as online facilities for students and lecturers follow upon registration.
Lecturers :	dr. K.S. Postek (Delft University of Technology), dr. J.C. Vera Lizcano (Tilburg University)

Course description:
(for participants of this course: see the lecturers' website)

Convexity plays an important role in optimization, particularly in nonlinear optimization. Many applications of optimization problems are nonlinear but have the convexity property. For convex optimization an elegant mathematical theory can be developed, including a duality theory and algorithmic aspects.

Key words for the course are: convex sets and functions; separation theorems; subdifferential calculus; polarity; Karush-Kuhn-Tucker theorem; duality; minimax results in game theory; optimal consumption and investment in economics.

Prerequisites:
Basic knowledge (bachelor level) of analysis and linear algebra.

Literature:
Lecture notes will be provided. Further literature (also as indication for the level of the course):

- M.S. Bazaraa, H.D. Sherali and C.M. Shetty, Nonlinear programming, theory and algorithms, 2nd edition, Wiley, 1993.

- Borwein, J. and A.S. Lewis, Convex analysis and nonlinear optimisation, 2nd edition, Springer-Verlag, New York, 2006.

- J. Brinkhuis. Convex Analysis for Optimization - A Unified Approach, Springer, 2020.

- R.T. Rockafellar, Convex analysis, Princeton University Press, 1970.

Examination:
Take home problems.

Address of the lecturers:
Dr. K.S. Postek
Delft Institute of Applied Mathematics, Van Mourik Broekmanweg 6 (Visitor address) 2628 XE Delft
Phone: 015 - 2784109
E-mail: K.S.Postek@tudelft.nl

Dr. J.C. Vera Lizcano
Department of Econometrics & OR CentER, Tilburg University, P.O. Box 90153, 5000 LE Tilburg
Phone: 013 - 4662478
E-mail: J.C.VeraLizcano@uvt.nl