Abstract (100 words or less): |  | We describe theoretical and algorithmic components of the branch-and-reduce approach to the global optimization of continuous, integer, and mixed-integer nonlinear programs. These include: a theory of convex extensions for the construction of closed form expressions of convex envelopes of nonlinear functions, an entirely linear-programming-based approach to global optimization, a theory of domain reduction, and proofs of finiteness for certain branching schemes. Applications from a variety of application areas will be reviewed and extensive computational results with BARON will be reported. |