A geometric integration approach to nonsmooth, nonconvex optimisation

Understand

The optimisation of nonsmooth, nonconvex functions without access to gradients is a particularly challenging problem that is frequently encountered, for example in model parameter optimisation problems.

• Bilevel optimisation of parameters is a standard setting in areas such as variational regularisation problems and supervised machine learning.
• We present efficient and robust derivative-free methods called randomised Itoh--Abe methods.
• These are generalisations of the Itoh--Abe discrete gradient method, a well-known scheme from geometric integration, which has previously only been considered in the smooth setting.