SCIP: Global Optimization of Mixed-Integer Nonlinear Programs in a Branch-and-Cut Framework

This paper describes the extensions that were added to the constraint integer programmingframework SCIP in order to enable it to solve convex and nonconvex mixed-integer nonlinearprograms (MINLPs) to global optimality. SCIP implements a spatial branch-and-bound algorithmbased on a linear outer-approximation, which is computed by convex overand underestimationof nonconvex functions. An expression graph representation of nonlinear constraints allowsfor bound tightening, structure analysis, and reformulation. Primal heuristics are employedthroughout the solving process to find feasible solutions early. We provide insights into theperformance impact of individual MINLP solver components via a detailed computational studyover a large and heterogeneous test set.