The main goal of this compact course (LSF entry) is to provide insight into the foundations and the state-of-the-art of the research area Complexity Reducing Formulations in Optimization. To this end, the foundations will be taught in a tutorial part with hands-on practical exercises. Participants are kindly asked to bring their own notebooks with a Matlab or Octave installation. The five day tutorial part will also include insight into Magdeburg state-of-the-art projects in the field of algebra, discrete geometry, optimization, and optimal control.
The course is organized by Sebastian Sager. Lectureres include Gennadiy Averkov, Rolf Findeisen, Martin Henk, Thomas Kahle, Volker Kaibel, and Stefan Streif from the OvGU.
|09h-13h||Kaibel: Introduction to extended formulations||Henk/Kaibel: Practical exercises||Sager: Lifting in nonlinear optimization and control||Findeisen/Streif: Lifting in optimal control||Averkov: Various types of positivstellensätze and their application for solving polynomial optimization problems|
|14h-18h||Henk: A rough guide to semi-algebraic sets and polynomial representations: introduction to some basics of (Convex) Real Algebraic Geometry, the Bröcker-Scheiderer theorem and its consequences||Kahle: Ideals, Varieties, and Macaulay2||Sager: Computer exercises||Findeisen/Streif: Computer exercises||Kürschner:
Introduction to model reduction,
Semi-active damping optimization via model reduction
Yue/Li/Feng: 1) Model order reduction (Krylov method) for basic linear systems, 2) Extension to multi-stage linear systems with application to ROM-based SMB optimization, 3) POD-based MOR for SMB with nonlinear isotherms and trust-region POD optimization for SMB, 4) New ideas for ROM-based optimization.
Course material can be found on this password restricted page.
The number of participants is limited and we will follow a first come, first served practice. Please send an email to if you want to participate or have any questions.