FB 6 Mathematik/Informatik

Institut für Mathematik


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SS 2019

22.05.2019 um 17:15 Uhr in 69/125

Prof. Dr. Timo de Wolff (Technische Universität Braunschweig)

An Introduction to Nonnegativity and Polynomial Optimization

In science and engineering we regularly face hard, nonlinear polynomial optimization problems.
Solving these problems is essentially equivalent to certifying nonnegativity of multivariate, real
polynomials – a key problem in real algebraic geometry since the 19th century.
In this talk, we discuss how to tackle such problems both from the perspective of algebra and
optimization.

05.06.2019 um 17:15 Uhr in 69/125

Prof. Dr. Dirk Lorenz (Technische Universität Braunschweig)

Analysis and Algorithms for Optimal Transport

How to move mass or goods from where they are to designated places in the most efficient way? This question was posed in geometrical terms by Gaspard Monge in the 18th century already. In the middle of the 20th century Leonid Kantorovich reformulated to problem in the language of measure theory and developed a solution theory (which actually earned him the Nobel prize in economics in 1975). In recent days there have been an increasing interest in the mathematics of optimal transport and computational tools have been developed which helped to make optimal transport applicable in fields like mathematical imaging, machine learning or inverse problems.

In this talk I will introduce various formulations of optimal transport problems (involving, e.g. dynamics of partial differential equations, minimization problems with static partial differential equations as constraints, linear programming, or matrix scaling). I will shortly speak about the analysis of the problems and then focus on the computational problem of developing practical algorithms.