Vertex Representation of Convex Hulls for Fast Evaluation of Boundary Constraints in Model-Based Calibration for Automotive Engines

  • Florin NaeEmail author
  • Hayato Waki
Conference paper
Part of the Mathematics for Industry book series (MFI, volume 28)


In the field of automotive engines calibration, generating a boundary model of an admissible operation domain, for instance, a convex hull, is a step often required when solving constrained optimization problems addressed by Model-Based Calibration (MBC) software suites, such as Model-Based Calibration Toolbox from MathWorks. However, depending on the amount of data modeled, generating a convex hull might become a computationally intensive process. This is due to the fact that the half-space representation of the convex hull is used. We discuss here an alternative representation of the convex hull, the vertex representation, which proves capable to reduce the computational cost for specific conditions. Numerical comparisons in this article are executed in MATLAB using MBC Toolbox commands and show that for a representative optimization problem, the vertex representation outperforms the half-space representation.


Convex hull Boundary modeling Optimization Model-based calibration Automotive engine MBC toolbox 



This article is based on discussion in workshops of the IMI Joint Research Projects “Research of Boundary Modeling” (Principal investigator: Mr. Satoru Watanabe, Toyota Motor Company) and “Research of Engine Calibration from the Viewpoint of Mathematical Science” (Principal investigator: Mr. Masahiro Satou, Honda Automobile R&D).


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Copyright information

© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.The MathWorks G.K. Nagoya OfficeNaka-ku, NagoyaJapan
  2. 2.Institute of Mathematics for Industry, Kyushu UniversityFukuokaJapan

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