Duality results for stationary problems of open pit mine planning in a continuous function framework

open pit mine planning problems are usually considered in a mixed integer programming context. characterizing each attainable profile by a continuous function yields a continuous framework. it allows for a more detailed modeling of slope constraints and other material properties of slanted layers. although the resulting nonlinear programming problems are in general non-convex and non-differentiable, they provide certain advantages as one can directly compute sensitivities of optimal solutions w.r.t. small data perturbations. in this work duality results are derived for the stationary problems of the continuous framework employing an additional condition called convex-likeness.