Geodesic
Well-posedness of optimization problems and Hausdorff metric on partial maps
Bollettino della Unione matematica italiana, Série 8, 9B (2006) no. 3, pp. 645-656 Cet article a éte moissonné depuis la source 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 $(\mathcal{P}, H_\rho)$. 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 $(\mathcal{P}, H_\rho)$ is investigated. 
@article{BUMI_2006_8_9B_3_a7,
     author = {Caterino, Alessandro and Ceppitelli, Rita and Hol\`a, \v{L}ubica},
     title = {Well-posedness of optimization problems and {Hausdorff} metric on partial maps},
     journal = {Bollettino della Unione matematica italiana},
     pages = {645--656},
     year = {2006},
     volume = {Ser. 8, 9B},
     number = {3},
     zbl = {1177.54012},
     mrnumber = {2274117},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BUMI_2006_8_9B_3_a7/}
}
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Caterino, Alessandro; Ceppitelli, Rita; Holà, Ľubica. Well-posedness of optimization problems and Hausdorff metric on partial maps. Bollettino della Unione matematica italiana, Série 8, 9B (2006) no. 3, pp. 645-656. http://geodesic.mathdoc.fr/item/BUMI_2006_8_9B_3_a7/