Second order methods for the solution of large scale nonlinear noisy problems

par Elisa Riccietti (IRIT Toulouse)

vendredi 7 févr. 2020, 10:30 → 11:30 Europe/Paris

XLIM Salle X.203

In this talk I will present new second-order optimization methods to solve large scale nonlinear problems affected by noise. We distinguish two particular classes of noisy problems depending on the source of the noise. The first class is that of ill-posed least-squares problems with noise on the data, whose stable solution is very challenging and requires the design of new regularizing strategies. We describe how to modify standard trust region methods to make them suitable to handle such problems. The second class is that of large scale problems with an expensive objective function. We propose to exploit approximations of the objective function of dynamic accuracy to reduce the computational cost. We design two types of new second-order methods (subsampled and multilevel) that are able to deal with the noise introduced by these approximations. We prove convergence and complexity guarantees for all methods and test them experimentally on real-life applications arising in geophysics, image registration, classification of large data sets, and deep neural network training. The proposed methods are shown to outperform state-of-the-art methods in terms of both numerical stability and computational cost.