A new solution strategy for multiparametric quadratic programming

• Published in: Computers & chemical engineering Vol. 164; no. C; p. 107882
• Main Authors: Narciso, Diogo A.C., Pappas, Iosif, Martins, F.G., Pistikopoulos, Efstratios N.
• Format: Journal Article
• Language: English
• Published: United Kingdom Elsevier Ltd 01-08-2022; Elsevier
• Subjects: Explicit model predictive control; Multiparametric programming; Quadratic programming; Quadratic programming; Multiparametric programming; Explicit model predictive control
• ISSN: 0098-1354; 1873-4375
• DOI: 10.1016/j.compchemeng.2022.107882

•Proposed parameter transformation yields mp-QP problems with special topology properties.•New solution strategy enabled by parameter transformation.•Solution delivered as two compact statements, or optionally, in the classic explicit format.•Significant improvements on speed of calculation and size of offline solutions.•New framework for the analysis and calculation of multiparametric problems.
An innovative paradigm is presented in this paper for convex multiparametric quadratic programming (mp-QP), and made possible by a convenient transformation of the vector of parameters, and expansion of the corresponding parameter space. Solutions of mp-QP problems are now presented in a highly compact form, in place of deriving explicit expressions for all critical regions and optimizer functions, as is the standard practice in the field. This represents two significant advantages over the state-of-the art mp-QP algorithms: firstly, this paradigm offers a much less expensive path for solution calculation; secondly, these compact solutions require minimal storage requirements. This is particularly significant for mp-QP problems including many inequality constraints, which can now be addressed with minimal computational burden. Compact solutions may then be explored to obtain the explicit solutions for the original mp-QP problems if required, where the original parameter dependence and bounds are recovered.