Abstract
In this paper we propose a reduced vertex result for the robust solution of uncertain semidefinite optimization problems subject to interval uncertainty. If the number of decision variables is m and the size of the coefficient matrices in the linear matrix inequality constraints is n×n, a direct vertex approach would require satisfaction of 2n(m+1)(n+1)/2 vertex constraints: a huge number, even for small values of n and m. The conditions derived here are instead based on the introduction of m slack variables and a subset of vertex coefficient matrices of cardinality 2n−1, thus reducing the problem to a practically manageable size, at least for small n. A similar size reduction is also obtained for a class of problems with affinely dependent interval uncertainty.
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Communicated by B.T. Polyak.
This work is supported by MIUR under the FIRB project “Learning, Randomization and Guaranteed Predictive Inference for Complex Uncertain Systems,” and by CNR RSTL funds.
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Calafiore, G., Dabbene, F. Reduced Vertex Set Result for Interval Semidefinite Optimization Problems. J Optim Theory Appl 139, 17–33 (2008). https://doi.org/10.1007/s10957-008-9423-1
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DOI: https://doi.org/10.1007/s10957-008-9423-1