Primal-Dual Enumeration for Multiparametric Linear Programming

  • Colin N. Jones
  • Jan M. Maciejowski
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4151)


Optimal control problems for constrained linear systems with a linear cost can be posed as multiparametric linear programs (pLPs) and solved explicitly offline. Several algorithms have recently been proposed in the literature that solve these pLPs in a fairly efficient manner, all of which have as a base operation the computation and removal of redundant constraints. For many problems, it is this redundancy elimination that requires the vast majority of the computation time. This paper introduces a new solution technique for multiparametric linear programs based on the primal–dual paradigm. The proposed approach reposes the problem as the vertex enumeration of a linearly transformed polytope and then simultaneously computes both its vertex and halfspace representations. Exploitation of the halfspace representation allows, for smaller problems, a very significant reduction in the number of redundancy elimination operations required, resulting in many cases in a much faster algorithm.


Model Predictive Control Tangent Cone Model Predictive Controller Support Cone Parametric Linear Program 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Colin N. Jones
    • 1
  • Jan M. Maciejowski
    • 2
  1. 1.Automatic Control LaboratorySwiss Federal Institute of TechnologyZurichSwitzerland
  2. 2.Control Group, Department of EngineeringUniversity of CambridgeCambridgeUK

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