  This work attempts to combine the strengths of two major technologies that
have matured over the last three decades: global mixed-integer nonlinear
optimization and branch-and-price. We consider a class of generally nonconvex
mixed-integer nonlinear programs (MINLPs) with linear complicating constraints
and integer linking variables. If the complicating constraints are removed, the
problem becomes easy to solve, e.g. due to decomposable structure. Integrality
of the linking variables allows us to apply a discretization approach to derive
a Dantzig-Wolfe reformulation and solve the problem to global optimality using
branch-and-price. It is a remarkably simple idea; but to our surprise, it has
barely found any application in the literature. In this work, we show that many
relevant problems directly fall or can be reformulated into this class of
MINLPs. We present the branch-and-price algorithm and demonstrate its
effectiveness (and sometimes ineffectiveness) in an extensive computational
study considering multiple large-scale problems of practical relevance, showing
that, in many cases, orders-of-magnitude reductions in solution time can be
achieved.
