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)[F A14], 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 a basis geometry improvement algorithm to adapt NOWPAC for the usage of RBFs. 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.     «

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)[F A14], 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 lo...     »