Nonconvex control and optimization problems for nonlinear dynamical systems can be approached with numerical methods inspired by operator theory. The workshop is an opportunity to present for the first time in a unified way two major operator theoretical approaches to nonlinear dynamical systems: Koopman operator methods for dynamical systems, relying on Galerkin numerical discretization techniques; polynomial optimization and optimal control formulated as generalized problems of moments, discretized by hierarchies of convex linear matrix inequalities, and solved numerically with semidefinite programming. These techniques are applied to compute regions of attraction and invariant sets, and to solve dynamical systems problems arising in neuroscience.