Abstract As rapid response to changes becomes more imperative, optimization under uncertainty has continued to grow in both the continuous and mixed-integer fields. We design a branch-and-bound (BB) algorithm for mixed-binary nonlinear optimization problems with parameters in general locations. At every node of the BB tree we apply a state-of-the-art algorithm we have recently developed to approximately optimize parametric programs containing objectives and constraints biconvex in the variables and parameters. Numerical results are included.