Neural network training under semidefinite constraints

This paper is concerned with the training of neural networks (NNs) under semidefinite constraints, which allows for NN training with robustness and stability guarantees. In particular, we set up an efficient and scalable training scheme for NN training problems of this kind based on interior point methods, while we also exploit the structure of the underlying matrix constraint. We apply our training scheme to several relevant examples that have been studied in the literature and newly present the application of the method to the training of Wasserstein generative adversarial networks (WGANs). In numerical examples, we show the superiority of our method and its applicability to WGAN training.