Introduction to Conic Optimization

Course title

Introduction to Conic Optimization.

Faculty

Erling D. Andersen. MOSEK ApS, Fruebjergvej 3, Box 16, 2100 Copenhagen, Denmark.

Dr. Erling D. Andersen is a founder and CEO of the Danish company MOSEK ApS that makes and sells optimization software since January 1999. Previously he was assistant professor at Odense University and took a two years post-doc stay at Delft University. The main of interests of Erling is mathematical optimization and in particular conic optimization. Erling has published several articles about optimization algorithms and related topics in leading international journals such as Mathematical Programming.

Email: e.d.andersen@mosek.com.Personal Web: http://erling.andersen.name. Company Web: http://www.mosek.com.

Course language

English.

Course schedule

June 20 and 21, from 10:00am to 1:00pm and from 3:00pm to 6:00pm.

June 22, from 10:00am to 1:00pm.

Description

Abstract

The course will provide the foundations and basic ideas of conic optimization, with a focus on second order conic (SOCO) and semidefinite optimization (SDO). Among the topics covered we find: modelling in conic optimization; duality in conic optimization; basic algorithms in conic optimization. The course includes discussion of some cases with implementation in MATLAB or Python using the MOSEK optimization engine.

Lecture plan

Lecture 1: Conic optimization. What is conic optimization and why is it interesting. Some examples. Duality theory for conic optimization: Duality; Infeasibility certificates; What can go wrong.

Lecture 2: Conic modelling. Which sets are conic representable.

Lecture 3: Case studies in conic modelling. Robust optimization. Portfolio optimization incl. implementation in MATLAB. Semidefinite optimization.

Lecture 4: Solving conic optimization problems. Algorithms for conic optimization problems. Software for conic optimization problems.

Lecture 5: A case study in conic optimization to be done by the students.

Reading material

The main background material used in the course are [2] and [1]. A hardcopy of the latter will be handed out in class.

References

[1] Mosek ApS. The MOSEK Modeling Cookbook. Fruebjergvej 3, Boks 16, 2100 Copenhagen O, 2012. Last revised September 2015.

[2] A. Nemirovski. Advances in convex optimization: Conic programming. In Marta Sanz-Sol, Javier Soria, Juan L. Varona, and Joan Verdera, editors, Proceedings of International Congress of Mathematicians, Madrid, August 22-30, 2006, Volume 1, pages 413 to 444. EMS - European Mathematical Society Publishing House, 2007.

Evaluation

The course will be evaluated through a case study to be solved in class.

Classroom

TBA