Randomized operator splitting schemes for abstract evolution equations by Monika Eisenmann, mathematics, LTH

Abstract evolution equations are an important building block for modeling processes in physics, biology and social sciences. Moreover, optimization problems can be reformulated into evolution equations. Their applications such as machine learning, benefit from randomized optimization methods like the stochastic gradient descent method. Such a stochastic optimizer can be interpreted as a randomized operator splitting scheme. While deterministic operator splitting methods are already a powerful tool in the approximation of evolution equations, we extend it to a randomized version.

In this talk, we propose a randomized operator splitting scheme in an abstract setting and exemplify the theory by considering a randomized domain decomposition scheme.