  In this paper, we consider the canonical water network design problem, which
contains nonconvex potential loss functions and discrete resistance choices
with varying costs. Traditionally, to resolve the nonconvexities of this
problem, relaxations of the potential loss constraints have been applied to
yield a more tractable mixed-integer convex program (MICP). However, design
solutions to these relaxed problems may not be feasible with respect to the
full nonconvex physics. In this paper, it is shown that, in fact, the original
mixed-integer nonconvex program can be reformulated exactly as an MICP.
Beginning with a convex program previously used for proving nonlinear network
design feasibility, strong duality is invoked to construct a novel, convex
primal-dual system embedding all physical constraints. This convex system is
then augmented to form an exact MICP formulation of the original design
problem. Using this novel MICP as a foundation, a global optimization algorithm
is developed, leveraging heuristics, outer approximations, and feasibility
cutting planes for infeasible designs. Finally, the algorithm is compared
against the previous relaxation-based state of the art in water network design
over a number of standard benchmark instances from the literature.
