Geometric algorithm for multiparametric linear programming

We propose a novel algorithm for solving multiparametric linear programming (LP) problems. Rather than visiting different bases of the associated LP tableau, we follow a geometric approach based on the direct exploration of the parameter space. The resulting algorithm has computational advantages, namely the simplicity of its implementation in a recursive form and an efficient handling of primal and dual degeneracy. Illustrative examples describe the approach throughout the paper. The algorithm is used to solve finite-time constrained optimal control problems for discrete-time linear dynamical systems.