  Non-convex optimal control problems occurring in, e.g., water or power
systems, typically involve a large number of variables related through
nonlinear equality constraints. The ideal goal is to find a globally optimal
solution, and numerical experience indicates that algorithms aiming for
Karush-Kuhn-Tucker points often find (near-)optimal solutions. In our paper, we
provide a theoretical underpinning for this phenomenon, showing that on a broad
class of problems the objective can be shown to be an invariantly convex
function (invex function) of the control decision variables when state
variables are eliminated using implicit function theory. In this way,
near-global optimality can be demonstrated, where the exact nature of the
global optimality guarantee depends on the position of the solution within the
feasible set. In a numerical example, we show how high-quality solutions are
obtained with local search for a river control problem where invexity holds.
