  In this paper, we investigate the performance of two first-order optimization
algorithms, obtained from forward Euler discretization of finite-time
optimization flows. These flows are the rescaled-gradient flow (RGF) and the
signed-gradient flow (SGF), and consist of non-Lipscthiz or discontinuous
dynamical systems that converge locally in finite time to the minima of
gradient-dominated functions. We propose an Euler discretization for these
first-order finite-time flows, and provide convergence guarantees, in the
deterministic and the stochastic setting. We then apply the proposed algorithms
to academic examples, as well as deep neural networks training, where we
empirically test their performances on the SVHN dataset. Our results show that
our schemes demonstrate faster convergences against standard optimization
alternatives.
