MATLAB Programm Repository DualityGapAnalyzer: The set of target vectors in a semi-infinite linear program with a duality gap. We propose a geometric method for the analysis of duality relations in a pair of semi-infinite linear programs (SILPs). The method is based on the use of the conic hull of the coefficients in the constraint system. A relation between the presence of a duality gap and the nonclosedness of the boundary of the conic hull of points in a multidimensional space is established. The geometric approach is used to construct an opposite pair of dual problems and to explore the duality relations for this pair. We construct a nontrivial example of a SILP in which the duality gap occurs for noncollinear target vectors.
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References in zbMATH (referenced in 2 articles , 1 standard article )
Showing results 1 to 2 of 2.
- Astaf’ev, N. N.; Ivanov, A. V.; Trofimov, S. P.: The set of target vectors in a semi-infinite linear program with a duality gap (2019)
- Goberna, M. A.; López, M. A.: Recent contributions to linear semi-infinite optimization: an update (2018)