Course CAO: Convex Analysis for Optimization

Time:	Monday 13.15 – 15.00 (September 9 – November 11) Please note that there is no lecture on 7 October
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):

• D. Bertsekas, Convex Optimization Theory, Athena Scientific, 2009.
• S. Boyd and L. Vandenberghe, Convex Optimization, Cambridge University Press, 2004.
• 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

Dr. Olga Kuryatnikova
Erasmus School of Economics
Erasmus University Rotterdam
Campus Woudestein
Burgemeester Oudlaan 50
3062 PA Rotterdam
E-mail: kuryatnikova@ese.eur.nl

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

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