Abstract.
We consider parametric semi-infinite optimization problems without the usual asssumptions on the continuity of the involved mappings and on the compactness of the index set counting the inequalities. We establish a characterization of those optimization problems which have a unique or strongly unique solution and which are stable under small pertubations. This result generalizes a well-known theorem of Nürnberger. The crucial roles in our investigations are a new concept of active constraints, a generalized Slater's condition, and a Kuhn—Tucker-type theorem. Finally, we give some applications in vector optimization, for approximation problems in normed spaces, and in the stability of the minimal value.
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Accepted 5 August 1996
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Helbig, S., Todorov, M. Unicity Results for General Linear Semi-Infinite Optimization Problems Using a New Concept of Active Constraints . Appl Math Optim 38, 21–43 (1998). https://doi.org/10.1007/s002459900080
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DOI: https://doi.org/10.1007/s002459900080