  We develop a bootstrap approach to Effective Field Theories (EFTs) based on
the concept of duality in optimisation theory. As a first application, we
consider the fascinating set of EFTs for confining flux tubes. The outcome of
our analysis are optimal bounds on the scattering amplitude of Goldstone
excitations of the flux tube, which in turn translate into bounds on the Wilson
coefficients of the EFT action. Finally, we comment on how our approach
compares to EFT positivity bounds.
