%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 comité 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 %~ UNIV-BREST %~ INSTITUT-TELECOM %~ ENSTA-BRETAGNE %~ CNRS %~ UNIV-UBS %~ ENSTA-BRETAGNE-STIC %~ ENIB %~ LAB-STICC %~ TDS-MACS %~ INSTITUTS-TELECOM