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.
Contractors and Linear Matrix Inequalities
Manuscript received October 25, 2014; final manuscript received June 3, 2015; published online July 1, 2015. Assoc. Editor: Alba Sofi.
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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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