Well-posedness of optimization problems and Hausdorff metric on partial maps
Caterino, Alessandro ; Ceppitelli, Rita ; Holà, Ľubica
Bollettino dell'Unione Matematica Italiana, Tome 9-A (2006), p. 645-656 / Harvested from Biblioteca Digitale Italiana di Matematica
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The object of this paper is the Hausdorff metric topology on partial maps with closed domains. This topological space is denoted by (𝒫,Hρ). An equivalence of well-posedness of constrained continuous problems is proved. By using the completeness of the Hausdorff metric on the space of usco maps with moving domains, the complete metrizability of (𝒫,Hρ) is investigated.

In questo lavoro si studiano alcune proprieta dello spazio (𝒫,Hρ) delle mappe parziali con dominio chiuso, munito della topologia della metrica di Hausdorff. Si prova un'equivalenza tra le definizioni di buona posizione secondo Tykhonov e Hadamard di problemi di minimizzazione continui e vincolati, dove la dipendenza continua è descritta dalla metrica di Hausdorff sulle mappe parziali. Lo studio della completezza della metrica di Hausdorff nello spazio delle multifunzioni usco con dominio variabile permette di individuare condizioni per la completa metrizzabilità di (𝒫,Hρ)

Publié le : 2006-10-01
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     author = {Alessandro Caterino and Rita Ceppitelli and \v Lubica Hol\`a},
     title = {Well-posedness of optimization problems and Hausdorff metric on partial maps},
     journal = {Bollettino dell'Unione Matematica Italiana},
     volume = {9-A},
     year = {2006},
     pages = {645-656},
     zbl = {1177.54012},
     mrnumber = {2274117},
     language = {en},
     url = {http://dml.mathdoc.fr/item/BUMI_2006_8_9B_3_645_0}
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Caterino, Alessandro; Ceppitelli, Rita; Holà, Ľubica. Well-posedness of optimization problems and Hausdorff metric on partial maps. Bollettino dell'Unione Matematica Italiana, Tome 9-A (2006) pp. 645-656. http://gdmltest.u-ga.fr/item/BUMI_2006_8_9B_3_645_0/

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