Dr. Michael Mühlebach’s research aims at exploiting analogies between dynamic systems and optimization. The underlying idea is the following: Consider the minimization of a two-dimensional function. Such a function can be visualized as a landscape of hills, and thus, in order to find a local minimum, one can simply place a marble in the landscape and let the marble roll downhill, accelerated by the gravitational pull. Provided that some friction is added, the marble will ultimately stop at a local minimum. Constraints are naturally implemented as barriers against which the marble can bounce off, resulting in non-smooth dynamics. As highlighted with the following example, such a perspective rooted in non-smooth dynamics, leads to a different treatment of constraints compared to standard optimization strategies. It might also contribute to a better understanding of optimization algorithms and has the potential to enable new algorithms that efficiently deal with large data sets.
