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In multiparametric programming an optimization problem which is dependent ona parameter vector is solved parametrically. In control, multiparametricquadratic programming (mp-QP) problems have become increasingly important sincethe optimization problem arising in Model Predictive Control (MPC) can be castas an mp-QP problem, which is referred to as explicit MPC. One of the mainlimitations with mp-QP and explicit MPC is the amount of memory required tostore the parametric solution and the critical regions. In this paper, a methodfor exploiting low rank structure in the parametric solution of an mp-QPproblem in order to reduce the required memory is introduced. The method isbased on ideas similar to what is done to exploit low rank modifications ingeneric QP solvers, but is here applied to mp-QP problems to save memory. Theproposed method has been evaluated experimentally, and for some examples ofrelevant problems the relative memory reduction is an order of magnitudecompared to storing the full parametric solution and critical regions.

Reduced Memory Footprint in Multiparametric Quadratic Programming by Exploiting Low Rank Structure