Combinatorial multi-parametric quadratic programming with saturation matrix based pruning

The goal of multi-parametric quadratic programming (mpQP) is to compute analytic solutions to parameter-dependent constrained optimization problems, e.g., in the context of explicit linear MPC. We propose an improved combinatorial mpQP algorithm based on a saturation matrix pruning criterion which uses geometric properties of the constraint polyhedron for excluding infeasible constraint combinations from the candidate active set enumeration. Performance improvements are discussed for both practical and random example problems from the area of explicit linear MPC.