A novel approach to multiparametric quadratic programming

Authors:
Arun Gupta;Sharad Bhartiya;P. S. V. Nataraj
Affiliations:
Department of Chemical Engineering, Indian Institute of Technology, Bombay, Powai, Mumbai 400076, India;Department of Chemical Engineering, Indian Institute of Technology, Bombay, Powai, Mumbai 400076, India;Systems and Control Engineering, Indian Institute of Technology, Bombay, Powai, Mumbai 400076, India
Venue:
Automatica (Journal of IFAC)
Year:
2011

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Abstract

Multiparametric (mp) programming pre-computes optimal solutions offline which are functions of parameters whose values become apparent online. This makes it particularly well suited for applications that need a rapid solution of online optimization problems. In this work, we propose a novel approach to multiparametric programming problems based on an enumeration of active sets and use it to obtain a parametric solution for a convex quadratic program (QP). To avoid the combinatorial explosion of the enumeration procedure, an active set pruning criterion is presented that makes the enumeration implicit. The method guarantees that all regions of the partition are critical regions without any artificial cuts, and further that no region of the parameter space is left unexplored.