Speaker
Description
We propose a method for the optimization of discontinuous functions, for which all discontinuities are contained along lower dimensional manifolds. Traditional methods construct a robust optimization problem by either sampling or smoothing indifferently over the entire parameter space. However, these methods suffer from exponentially increasing cost for an increasing size of the parameter set. The key to our method is to approximate the globally smoothed objective function through a local smoothing function, which is applied in the vicinity of the discontinuity only. The function exploits the structure of the discontinuity set to dynamically detect location and orientation of the discontinuity. Consequently, integration is restricted to a low dimensional space, namely the one-dimensional line perpendicular to the discontinuity set. We show that this smoothing function is continuously differentiable on the parameter space and demonstrate the performance for the discussed setting. Furthermore, we demonstrate a significant reduction in computational cost when comparing our method with a globally smoothing approach. Additionally, we propose a method for detection of discontinuities by tracking the minimal eigenvalue for problems, for which the objective function relies on the evaluation of another energy minimization problem.
