MAGDEBURG LECTURES

ON OPTIMIZATION AND CONTROL

 Uncertainty quantification in inverse problems

Prof. Dr. Claudia Schillings
Universität Mannheim

Time & Place
The presentation on June 27, 2017 will be given in the Lukasklause (Schleinufer 1, 39104 Magdeburg) and starts at 5.00 p.m. (Großer Saal).

Abstract
Uncertainty quantification is an interesting, fast growing research area aiming at developing methods to address, characterize and minimize the impact of parameter, data and model uncertainty in complex systems. Applications of uncertainty quantification include all areas of engineering, environmental, physical and biological systems, e.g., groundwater flow problems, shape uncertainties in aerodynamic applications or nano-optics, biochemical networks and finance. The efficient treatment of uncertainties in mathematical models requires ideas and tools from various disciplines including numerical analysis, statistics, probability and computational science. In this talk, we will focus on the identification of parameters through observations of the response of the system - the inverse problem. The uncertainty in the solution of the inverse problem will be described via the Bayesian approach. We will discuss efficient methods to approximate the solution of the resulting high/ infinite dimensional systems.

Magdeburg Lectures on Optimization and Control

Prof. Dr. Zlatko Drmac
University of Zagreb

Accurate linear algebra in computational
methods for system and control theory

Tuesday, 05.07.2016 17:00
Lukasklause, Schleinufer 1

Jointly organized by: Faculty of Electrical Engineering and Information Technology, Faculty of Mathematics, Max Planck Institute Magdeburg Center for Dynamic Systems: Biosystems Engineering

Global Optimization of Unconventional Formulations for Sustainable Energy Systems 

Prof. Dr. Alexander Mitsos

RWTH Aachen University

Time & Place

The presentation on May 3, 2016 will be given at the Lukasklause, Schleinufer 1, Magdeburg and starts at 5.00 p.m.

Abstract

The presentation gives an overview of the group's recent and current work on energy systems and describes some highlights in more detail. The focus is on the optimal design of renewable energy systems, in particular concentrated solar thermal, geothermal and biomass conversion. We discuss optimal layout, optimal design and optimal operation over time scales (hourly, daily, seasonal). We also discuss hybrid systems consisting of more than one energy source with the goal of synergetically combining sources with different characteristics. These systems have characteristics that are different from conventional energy systems, namely the combination of turbomachinery and chemical processes, pronounced uncertainty and time-variability. As a result, these systems need to be addressed using systematic methods from process systems engineering and at the same time can be utilized to identify and overcome limits in these methodologies. In the last decade, algorithms for deterministic global optimization of mixed-integer nonlinear programs (MINLP) have undergone major changes rendering the solution of challenging optimization problems possible. We utilize these advantages to optimize several renewable energy systems using state-of-the-art codes. However, we also demonstrate that the optimization of several systems is not possible using these codes due to mainly two reasons, namely scaling of computational complexity with size of problems and the fact that natural formulations for many problems do not follow the traditional MINLP. To address these problems we develop theory for the scaling of algorithms and algorithms for unconventional formulations and utilize them for energy systems. In particular we discuss embedded/hierarchical programs (bilevel, semi-infinite, differential-algebraic systems with optimization embedded) and how these problems can be solved. We finally briefly discuss open challenges in optimization theory and algorithms and in energy systems.

Short CV

Alexander Mitsos is a Full Professor (W3) in RWTH Aachen University, and the Director of the Laboratory for Process Systems Engineering (AVT.SVT), comprising 40 research and administrative staff. Mitsos received his Dipl-Ing from University of Karlsruhe in 1999 and his Ph.D. from MIT in 2006, both in Chemical Engineering. Prior appointments include military service, free-lance engineering, involvement in a start-up company, a junior research group leader position in the Aachen Institute of Computational Engineering Science and the Rockwell International Assistant Professorship at MIT. Mitsos has over 80 peer-reviewed publications and has received a number of awards. His research focuses on optimization of energy and chemical systems and development of enabling numerical algorithms.

Concepts of Function Space Oriented Optimization

Prof. Dr. Anton Schiela
University of Bayreuth

Time & Place
The presentation on January 12, 2016 will be given at the Lukasklause, Schleinufer 1, Magdeburg and starts at 5.00 p.m.

Abstract
Many large scale nonlinear optimization problems are discretizations of
optimization problems in function space and thus, we expect that additional
functional analytic structure should be present. The goal of function space
oriented optimization is to exploit this structure. This may comprise the
efficient computation of steps by iterative solvers, problem suited
globalization strategies, or the use of adaptive mesh refinement inside
an optimization method.

In this talk we will give an overview of a couple of ideas, and explain at
concrete examples how they can be implemented.

Short CV
Anton Shiela is a professor for applied mathematics at the University of Bayreuth.

His fields of research are optimization with PDEs, in particular the
development of algorithms for the solution of optimization problems in
function space.

Before moving to Bayreuth in 2014, he was an associate professor
at Technische Universitaet Hamburg-Harburg (2013-2014) and
Matheon junior reseach group leader at TU Berlin (2012-2013).
He got his PhD in 2007 at Zuse Institute Berlin, where he worked
as a reasearch assistant (2002-2012).

No Small Linear Program Approximates Vertex Cover within a Factor 2-ε

Prof. Dr. Samuel Fiorini
Université Libre de Bruxelles

Time & Place
The presentation on December 8, 2015 will be given at the Lukasklause, Schleinufer 1, Magdeburg and starts at 5.00 p.m.

Abstract
The vertex cover problem is one of the most important and intensively studied combinatorial optimization problems. Khot and Regev (2003) proved that the problem is NP-hard to approximate within a factor 2-ε, assuming Khot's famous Unique Games Conjecture (UGC). This is tight because the problem has an easy 2-approximation algorithm.

We prove the following unconditional result about linear programming (LP) relaxations of the problem: every LP relaxation that approximates vertex  cover within a factor 2-ε has super-polynomially many inequalities.

Nonnegative Polynomials and Sum of Squares

Prof. Greg Blekherman, Ph.D.
Georgia Tech

Time & Place
The presentation on June 30, 2015 will be given in the Otto-von-Guericke-University Magdeburg G03-214 and starts at 5.00 p.m.

Abstract
A polynomial with real coefficients is nonnegative if it takes only nonnegative values. For example, any sum of squares is obviously nonnegative. The study of the relationship between nonnegative polynomials and sums of squares is a classical area in real algebraic geometry. It also has many applications, for instance in optimization and control theory, where sums of squares can be used for construction of Lyapunov functions, and understanding the size of semidefinite lifts of combinatorial optimization polytopes. After reviewing the history of the problem I will explain how this topic is inextricably linked to classical topics in complex algebraic geometry (varieties of minimal degree, dimension of secant varieties). Surprisingly these connections come via convex geometry. The talk is based on joint work with Sadik Iliman, Martina Kubitzke, Greg Smith and Mauricio Velasco.