Global optimization and constraint satisfaction: The branch-and-reduce approach

In the early 1990s, we proposed the integration of constraint programming and optimization techniques within the branch-and-bound framework for the global optimization of nonconvex nonlinear and mixed-integer nonlinear programs. This approach, referred to as branch-and-reduce, was subsequently supplemented with a variety of branching and bounding schemes. In this paper, we review the theory and algorithms behind branch-and-reduce, its implementation in the BARON software, and some recent successful applications.