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Farkas-type theorems for positively homogeneous semi-infinite systems. (English) Zbl 1077.90072

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.

MSC:

90C34 Semi-infinite programming
49N15 Duality theory (optimization)
90C46 Optimality conditions and duality in mathematical programming
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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
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