A model-based trust-region algorithm for DFO and its adaptation to handle noisy functions and gradients

Abstract

The software BCDFO (Bound-Constrained Derivative-Free Optimization) was developed to improve the existing state-of-the-art software packages NEWUOA and BOBYQA which have been developed by M. Powell. But a known drawback of DFO methods is the difficulty to cope with higher dimensional problems. As many applications provide some sort of first order information, we propose here to add to our code BCDFO the possibility of handling (possibly noisy) gradient information. This information will be introduced in the local surrogate using weak constraints, where the weights will be proportional to the (known or estimated) error magnitude that corrupts the gradient.