Reduced Vertex Set Result for Interval Semidefinite Optimization Problems |
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Authors: | G Calafiore and F Dabbene |
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Institution: | (1) Dipartimento di Automatica e Informatica, Politecnico di Torino, Torino, Italy;(2) IEIIT-CNR, Politecnico di Torino, Torino, Italy |
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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 2
n(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 2
n−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.
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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Keywords: | Semidefinite optimization Robustness Linear matrix inequalities Uncertainty |
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