Ellipsoidal arithmetic for multivariate systems


  • M.E. Villanueva, J. Rajyaguru, B. Houska, B. Chachuat


  • Computer Aided Chemical Engineering
    Volume 37, pages 767 - 772, 2015.


The ability to determine enclosures for the image set of nonlinear functions is pivotal to many applications in engineering. This paper presents a method for the systematic construction of ellipsoidal extensions of factorable functions. It proceeds by lifting the ellipsoid to a higher dimensional space for every atom operation in the function DAG, thereby accounting for dependencies. We present theoretical results regarding the quadratic Hausdorff convergence of the computed enclosures. Moreover, we propose an efficient implementation, whereby the shape matrix of the lifted ellipsoid is stored in sparse format, and every atom operation corresponds to a sparse update in that matrix. We illustrate these developments with two numerical examples.



author = {M.E. Villanueva and J. Rajyaguru and B. Houska and B. Chachuat},
title = {Ellipsoidal arithmetic for multivariate systems},
journal = {Computer Aided Chemical Engineering},
year = {2015},
volume = {37},
pages = {767–772}