Abstract
In this paper, we show that the problem of computing the smallest interval submatrix of a given interval matrix [A] which contains all symmetric positive semi-definite (PSD) matrices of [A], is a linear matrix inequality (LMI) problem, a convex optimization problem over the cone of positive semidefinite matrices, that can be solved in polynomial time. From a constraint viewpoint, this problem corresponds to projecting the global constraint PSD (A) over its domain [A]. Projecting such a global constraint, in a constraint propagation process, makes it possible to avoid the decomposition of the PSD constraint into primitive constraints and thus increases the efficiency and the accuracy of the resolution.
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D. Henrion acknowledges support of grant No. 102/02/0709 of the Grant Agency of the Czech Republic, and project No. ME 698/2003 of the Ministry of Education of the Czech Republic.
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Jaulin, L., Henrion, D. Contracting Optimally an Interval Matrix without Loosing Any Positive Semi-Definite Matrix Is a Tractable Problem. Reliable Comput 11, 1–17 (2005). https://doi.org/10.1007/s11155-005-5939-3
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DOI: https://doi.org/10.1007/s11155-005-5939-3