ARGONAUT: algorithms for global optimization of constrained grey-box computational problems. The algorithmic framework ARGONAUT is presented for the global optimization of general constrained grey-box problems. ARGONAUT incorporates variable selection, bounds tightening and constrained sampling techniques, in order to develop accurate surrogate representations of unknown equations, which are globally optimized. ARGONAUT is tested on a large set of test problems for constrained global optimization with a large number of input variables and constraints. The performance of the presented framework is compared to that of existing techniques for constrained derivative-free optimization.