Reduced Vertex Set Result for Interval Semidefinite Optimization Problems

G. Calafiore () and F. Dabbene ()
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G. Calafiore: Politecnico di Torino
F. Dabbene: Politecnico di Torino

Journal of Optimization Theory and Applications, 2008, vol. 139, issue 1, No 2, 17-33

Abstract: 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.

Keywords: Semidefinite optimization; Robustness; Linear matrix inequalities; Uncertainty (search for similar items in EconPapers)
Date: 2008
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DOI: 10.1007/s10957-008-9423-1

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