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Contractors and Linear Matrix Inequalities

Jeremy Nicola 1, 2 Luc Jaulin 1, 2
STIC - Pôle STIC [Brest]
Lab-STICC - Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance
Abstract : 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. Read More:
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Contributeur : Annick Billon-Coat <>
Soumis le : jeudi 3 septembre 2015 - 12:51:50
Dernière modification le : mercredi 5 août 2020 - 03:50:11



Jeremy Nicola, Luc Jaulin. Contractors and Linear Matrix Inequalities. ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part B: Mechanical Engineering, American Society of Mechanical Engineers (ASME), 2015, Journal of Risk and Uncertainty in Engineering Systems, Part B: Mechanical Engineering, 1 (3), ⟨10.1115/1.4030781⟩. ⟨hal-01192706⟩



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