Abstract
Let (F,
, ○) be a complete, extremal, fully-ordered group with zero-element (introduced in HELBIG [5]). The aim of this paper is to consider optimization problems in (F n,
, ○) described by functions, which are linear with respect to
and ○, and to investigate their continuous dependence on the restriction vector. We derive necessary and sufficient conditions for the lower- and upper-semi-continuity and the closedness of the feasible-set-mapping. Finally, an application of such problems in some scheduling problems is given.
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© 1988 Birkhäuser Verlag Basel
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Helbig, S. (1988). Parametric semi-infinite optimization in certain lattices: Continuity of the feasible set. In: Hoffmann, KH., Zowe, J., Hiriart-Urruty, JB., Lemarechal, C. (eds) Trends in Mathematical Optimization. International Series of Numerical Mathematics/Internationale Schriftenreihe zur Numerischen Mathematik/Série internationale d’Analyse numérique, vol 84. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9297-1_8
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DOI: https://doi.org/10.1007/978-3-0348-9297-1_8
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-0348-9984-0
Online ISBN: 978-3-0348-9297-1
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