Open problems for tractability of multivariate integration

AbstractWe present a number of open problems regarding the tractability of multivariate integration for various spaces of functions in the worst case and randomized settings. In the worst case setting, we discuss two spaces. The first is a space of infinitely differentiable functions for which the tractability of multivariate integration is open. The second is a weighted tensor product Sobolev space for which necessary and sufficient conditions for tractability of multivariate integration are known. For this space, the exact value of the exponent of strong tractability is unknown, and determining this exponent is open. We end this note by presenting an open problem for the tractability of multivariate integration in the randomized setting