Convex and concave relaxations are used extensively in global optimization algorithms.
Among the various techniques available for generating relaxations of a given function …

A new method for evaluating generalized derivatives in nonsmooth problems is reviewed.
Lexicographic directional (LD-) derivatives are a recently developed tool in nonsmooth …

This paper presents a framework for constructing and analyzing enclosures of the reachable
set of nonlinear ordinary differential equations using continuous-time set-propagation …

A novel subgradient evaluation method is proposed for nonsmooth convex relaxations of
parametric solutions of ordinary differential equations (ODEs) arising in global dynamic …

Hammerstein–Wiener models constitute a significant class of block-structured dynamic
models, as they approximate process nonlinearities on the basis of input–output data …

This paper gives an overview of recent developments in set-theoretic methods for nonlinear
systems, with a particular focus on the activities in our own research group. Central to these …

This paper presents a branch-and-lift algorithm for solving optimal control problems with
smooth nonlinear dynamics and potentially nonconvex objective and constraint functionals …

Novel convex and concave relaxations are proposed for the solutions of parametric ordinary
differential equations (ODEs), to aid in furnishing bounding information for deterministic …

This paper presents a discretize-then-relax method to construct convex/concave bounds for
the solutions of a wide class of parametric nonlinear ODEs. The algorithm builds upon …

In this work, we present general methods to construct convex/concave relaxations of the
activation functions that are commonly chosen for artificial neural networks (ANNs). The …