Mathematical Complexity Reduction - Otto-von-Guericke-University Magdeburg


Compact course Optimization

The compact course Mathematical Complexity Reduction: Optimization (LSF) will be held within SS 2017 for PhD students of the Research Training Group. Interested master and PhD students, e.g., from the Faculty of Mathematics or the IMPRS, may also participate if places are available (Wahlfach).

The main goal of this compact course is to provide insight into the state of the art of the research area Optimization. To this end, the foundations will be taught in a tutorial part with hands-on practical exercises. In addition, a more detailed exposition of complexity reduction aspects will be given.

The block course will build on a compact overview of deterministic optimization algorithms for Linear Optimization, Nonlinear Optimization, Polynomial Optimization, Mixed-integer Nonlinear Optimization, and Dynamic Optimization. The focus of the complexity reduction part will be on approximation hierarchies and their relation to Positivstellensätze, and lifting, such as the Lifted Newton method.

The theoretic overview will be complemented by practical hands-on exercises on participants' notebooks. Please bring your notebook, ideally with Matlab or Octave already installed. Using AMPL or CasADi is optional. You can download slides, exercise sheets, AMPL executables and more from this password protected page.


The course is organized and taught by Gennadiy Averkov and Sebastian Sager.

Preliminary program

The preliminary program reads as follows.

First part, lectures given by Sebastian Sager.

Time Mon, June 26 Tue, June 27 Wed, June 28 Thu, June 29 Fri, June 30
09h15 Introduction Nonlinear Optimization Nonlinear Optimization Lifted Optimization Global optimization
10h15 Exercises Exercises Exercises Exercises Exercises
11h15 Break
11h30 Linear Optimization Nonlinear Optimization Lifted Optimization Lifted Optimization Mixed-Integer Nonlinear Optimization
12h30 Exercises Exercises Exercises Exercises Exercises
13h30 Lunch

In addition, there will be a talk within the MALOC lecture series on Tuesday, 17h00, in the Lukasklause, which is part of the compact course. Claudia Schillings is talking about Uncertainty quantification in inverse problems.

Second part, lectures given by Gennadiy Averkov.

Time Mon, July 3 Tue, July 4 Wed, July 5 Thu, July 6 Fri, July 7
8:00-9:30 Introduction Real Algebra Stellensätze Conic Optimization Interior-point methods for semidefinite optimization
10:00-11:30 Real algebra Stellensätze Conic optimization Semidefinite optimization Software session (Baron, Sedumi etc.)
12:30-13:30 Real algebra Exercises Exercises Exercises Software session

Please send an email to if you want to participate.