SCCS Colloquium - Sep 25, 2019
|Date:||September 25, 2019|
|Time:||15:00 - 16:00|
Jonas Donhauser: Radial Basis Function Surrogates for Derivative-Free Optimization in NOWPAC
This is a Bachelor's thesis submission talk. Jonas is advised by Friedrich Menhorn.
Radial Basis Function (RBF) interpolation has become a popular interpolation method in many scientific fields, due to several useful mathematical properties. We will present a modified variant of the derivative free optimization algorithm NOWPAC (Nonlinear Optimization With Path-Augmented Constraints), using RBF surrogate models instead of the native quadratic model.
Since the amount of black box evaluations should be as low as possible, the surrogate model is supposed to offer a good local approximation of the objective function and constraints by using as few black box evaluations as possible. Due to the trade off between using few interpolation points and getting a good approximation, the choice of the surrogate model for an optimization algorithm is highly critical for its convergence speed.
In this thesis relations between the geometry of interpolation nodes and model quality are discussed. Further we will describe an basis geometry improvement algorithm to adapt NOWPAC for the usage of RBFs.
Lastly the performance of NOWPAC using different surrogates is compared to different solvers against optimization on of the Rosenbrock function and selected test problems from the Hock-Schittkowski Benchmark. Together with the results, tests for the local approximation error, using different RBF kernel shapes, are provided.
Keywords: Derivative Free Optimization, Radial Basis Functions, NOWPAC
Fabio Madge: Parareal Algorithm for Circuit Simulation
We introduce the Parareal algorithm for parallel-in-time integration. Later we show how to apply it to the problem of analog circuit simulation.
Keywords: parallel-in-time integration