Over the last two decades so-called set oriented numerical methods have been developed in the context of the numerical treatment of dynamical systems. The basic idea is to cover the objects of interest - for instance invariant sets or invariant measures - by outer approximations which are created via multilevel subdivision techniques. At the beginning of this century these methods have been modified in such a way that they are also applicable to the numerical treatment of multiobjective optimization problems. Due to the fact that they are set oriented in nature these techniques allow for the direct computation of the entire so-called Pareto set. In this talk recent developments in the area of set oriented numerics will be presented both for dynamical systems and optimization problems. The reliability of these methods will be demonstrated by several applications such as the approximation of transport processes in ocean dynamics, or the optimization of a cruise control with respect to energy consumption and travel distance. Moreover a new algorithmic idea will be described which allows to compute invariant sets directly by Newton's method.
Set Oriented Numerical Methods for Dynamical Systems and Optimization
Michael Dellnitz, Univ. of Paderborn, Germany
Nov 3 2014 - 4:30pm