Linear matrix inequalities (LMIs) comprise a large class of convex constraints. Boxes, ellipsoids, and linear constraints can be represented by LMIs. The intersection of LMIs are also classified as LMIs. Interior-point methods are able to minimize or maximize any linear criterion of LMIs with complexity, which is polynomial regarding to the number of variables. As a consequence, as shown in this paper, it is possible to build optimal contractors for sets represented by LMIs. When solving a set of nonlinear constraints, one may extract from all constraints that are LMIs in order to build a single optimal LMI contractor. A combination of all contractors obtained for other non-LMI constraints can thus be performed up to the fixed point. The resulting propogation is shown to be more efficient than other conventional contractor-based approaches.
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September 2015
Research Papers
Contractors and Linear Matrix Inequalities
Jeremy Nicola,
Jeremy Nicola
Lab STICC, ENSTA Bretagne
, 2 Rue Francois Verny, 29806 Brest Cedex 9
, France
e-mail: jeremy.nicola@ensta-bretagne.org
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Luc Jaulin
Luc Jaulin
Lab STICC, ENSTA Bretagne
, 2 Rue Francois Verny, 29806 Brest Cedex 9
, France
e-mail: luc.jaulin@ensta-bretagne.org
Search for other works by this author on:
Jeremy Nicola
Lab STICC, ENSTA Bretagne
, 2 Rue Francois Verny, 29806 Brest Cedex 9
, France
e-mail: jeremy.nicola@ensta-bretagne.org
Luc Jaulin
Lab STICC, ENSTA Bretagne
, 2 Rue Francois Verny, 29806 Brest Cedex 9
, France
e-mail: luc.jaulin@ensta-bretagne.orgManuscript received October 25, 2014; final manuscript received June 3, 2015; published online July 1, 2015. Assoc. Editor: Alba Sofi.
ASME J. Risk Uncertainty Part B. Sep 2015, 1(3): 031004 (6 pages)
Published Online: July 1, 2015
Article history
Received:
October 25, 2014
Revision Received:
June 3, 2015
Accepted:
June 4, 2015
Online:
July 1, 2015
Citation
Nicola, J., and Jaulin, L. (July 1, 2015). "Contractors and Linear Matrix Inequalities." ASME. ASME J. Risk Uncertainty Part B. September 2015; 1(3): 031004. https://doi.org/10.1115/1.4030781
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