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

TL;DR

This paper introduces a method to significantly reduce memory usage in multiparametric quadratic programming by exploiting low rank structures, enhancing explicit MPC implementations.

Contribution

The paper presents a novel approach to exploit low rank structures in mp-QP solutions, substantially decreasing memory requirements compared to traditional methods.

Findings

Achieved up to an order of magnitude memory reduction

Validated method on relevant problem examples

Demonstrated effectiveness in explicit MPC contexts

Abstract

In multiparametric programming an optimization problem which is dependent on a parameter vector is solved parametrically. In control, multiparametric quadratic programming (mp-QP) problems have become increasingly important since the optimization problem arising in Model Predictive Control (MPC) can be cast as an mp-QP problem, which is referred to as explicit MPC. One of the main limitations with mp-QP and explicit MPC is the amount of memory required to store the parametric solution and the critical regions. In this paper, a method for exploiting low rank structure in the parametric solution of an mp-QP problem in order to reduce the required memory is introduced. The method is based on ideas similar to what is done to exploit low rank modifications in generic QP solvers, but is here applied to mp-QP problems to save memory. The proposed method has been evaluated experimentally, and for some examples of relevant problems the relative memory reduction is an order of magnitude compared to storing the full parametric solution and critical regions.