%0 Journal Article
%T Contractors and Linear Matrix Inequalities
%+ Lab-STICC_ENSTAB_CID_IHSEV ; OSM
%+ Lab-STICC_ENSTAB_CID_PRASYS
%A Nicola, Jeremy
%A Jaulin, Luc
%< avec comitÃ© de lecture
%@ 2332-9017
%J ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part B: Mechanical Engineering
%I American Society of Mechanical Engineers (ASME)
%S Journal of Risk and Uncertainty in Engineering Systems, Part B: Mechanical Engineering
%V 1
%N 3
%P xx
%8 2015-09-01
%D 2015
%R 10.1115/1.4030781
%K interval analysis
%K linear matrix inequality
%K contractor programming
%K convex optimization
%K constraint propagation
%K robotics Read More: http://ascelibrary.org/doi/abs/10.1115/1.4030781
%Z Engineering Sciences [physics]/AutomaticJournal articles
%X 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: http://ascelibrary.org/doi/abs/10.1115/1.4030781
%G English
%L hal-01192706
%U https://hal.science/hal-01192706
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