A novel approach to multiparametric quadratic programming

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...

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Bibliographic Details
Published in:Automatica (Oxford) 2011-09, Vol.47 (9), p.2112-2117
Main Authors: Gupta, Arun, Bhartiya, Sharad, Nataraj, P.S.V.
Format: Article
Language:English
Subjects:
Applied sciences
Combinatorial analysis
Enumeration
Exact sciences and technology
Explosions
Mathematical programming
Multiparametric programming
On-line systems
Online
Operational research and scientific management
Operational research. Management science
Optimization
Programming
Quadratic programming
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Summary: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.
ISSN:0005-1098
1873-2836
DOI:10.1016/j.automatica.2011.06.019