López, Marco A.; Martínez-Legaz, Juan E. Farkas-type theorems for positively homogeneous semi-infinite systems. (English) Zbl 1077.90072 Optimization 54, No. 4-5, 421-431 (2005). The article deals with systems of infinitely many inequalities involving functions that are positively homogeneous over a nonempty convex cone of the Euclidean space. The authors apply generalized convex conjugation theory to derive a Farkas-type and a Gale-type theorem for this kind of systems. The results are applied to linear and min-type inequality systems. Reviewer: Oliver Stein (Aachen) Cited in 7 Documents MSC: 90C34 Semi-infinite programming 49N15 Duality theory (optimization) 90C46 Optimality conditions and duality in mathematical programming Keywords:Farkas-type theorems; positively homogeneous functions; generalized convex conjugation; semi-infinite inequality systems; linear systems; min-type systems PDFBibTeX XMLCite \textit{M. A. López} and \textit{J. E. Martínez-Legaz}, Optimization 54, No. 4--5, 421--431 (2005; Zbl 1077.90072) Full Text: DOI References: [1] Rubinov AM, Journal of Convex Analysis 2 pp 309– (1995) [2] Rubinov AM, Abstract Convexity and Global Optimization (2000) [3] Kutateladze SS, Soviet Mathematics Doklady 12 pp 665– (1971) [4] DOI: 10.1137/0316018 · Zbl 0397.46013 · doi:10.1137/0316018 [5] DOI: 10.1023/A:1022602223919 · Zbl 0955.90105 · doi:10.1023/A:1022602223919 [6] Rockafellar RT, Convex Analysis (1970) [7] DOI: 10.1081/NFA-200052006 · Zbl 1072.90044 · doi:10.1081/NFA-200052006 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.