Course CAO: Convex Analysis for Optimization

Time:	Monday 13.15 - 15.00 (September 9 - November 11)
Location:	All LNMB courses take place on the Campus Utrecht Science Park. Room HFG 611, Hans-Freudenthal building, Budapestlaan 6, 3584 CD Utrecht
Lecturers:	Dr. Olga Kuryatnikova (Erasmus University), Prof. Dr. J.C. Vera Lizcano (Tilburg University)

Important information

Participants of this course: please see the lecturers' website.

Course description

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.

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

Prerequisites:

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

Examination:

Take home problems.

Address of the lecturers:

[tba]

Prof. 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