A Geometric Integration Approach to Nonsmooth, Nonconvex Optimisation

• DOI: 10.1007/s10208-020-09489-2
• Publication Date: 2021-07-29T22:02:26Z
• Authors: Erlend S. Riis; Matthias J. Ehrhardt; G. R. W. Quispel; Carola-Bibiane Sc...
• Keywords: Iterated function; Stationary point

Abstract The optimisation of nonsmooth, nonconvex functions without access to gradients is a particularly challenging problem that frequently encountered, for example in model parameter problems. Bilevel parameters standard setting areas such as variational regularisation problems and supervised machine learning. We present efficient robust derivative-free methods called randomised Itoh–Abe methods. These are generalisations the discrete gradient method, well-known scheme from geometric integration, which has previously only been considered smooth setting. demonstrate method its favourable energy dissipation properties well defined nonsmooth Furthermore, we prove whenever objective function locally Lipschitz continuous, iterates almost surely converge connected set Clarke stationary points. an implementation methods, apply it various test numerical results indicate can be superior state-of-the-art solving while still remaining competitive terms efficiency.