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Reduced Vertex Set Result for Interval Semidefinite Optimization Problems.
- Source :
- Journal of Optimization Theory & Applications; Oct2008, Vol. 139 Issue 1, p17-33, 17p, 1 Graph
- Publication Year :
- 2008
-
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<superscript> n( m+1)( n+1)/2</superscript> 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<superscript> n−1</superscript>, 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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00223239
- Volume :
- 139
- Issue :
- 1
- Database :
- Complementary Index
- Journal :
- Journal of Optimization Theory & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 35076154
- Full Text :
- https://doi.org/10.1007/s10957-008-9423-1