Geodesic
Upper Hölder Continuity of Minimal Points
Journal of convex analysis, Tome 9 (2002) no. 2, pp. 327-338.

Voir la notice de l'article provenant de la source Heldermann Verlag

We derive criteria for upper Lipschitz/Hölder continuity of the set of minimal points of a given subset A of a normed space Y when A is subjected to perturbations. To this aim we introdue the rate of containment of A, a real-valued function of one real variable, which measures the depart from minimality as a function of the distance from the minimal point set. The main requirement we impose is that for small arguments the rate of containment is a sufficiently fast growing function. The obtained results are applied to parametric vector optimization problems to derive conditions for upper Hölder continuity of the performance multifunction.
Mots-clés : Minimal points, Hölder multivalued mappings, parametric vector optimization 
@article{JCA_2002_9_2_JCA_2002_9_2_a1,
     author = {E. M. Bednarczuk},
     title = {Upper {H\"older} {Continuity} of {Minimal} {Points}},
     journal = {Journal of convex analysis},
     pages = {327--338},
     publisher = {mathdoc},
     volume = {9},
     number = {2},
     year = {2002},
     url = {http://geodesic.mathdoc.fr/item/JCA_2002_9_2_JCA_2002_9_2_a1/}
}
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E. M. Bednarczuk. Upper Hölder Continuity of Minimal Points. Journal of convex analysis, Tome 9 (2002) no. 2, pp. 327-338. http://geodesic.mathdoc.fr/item/JCA_2002_9_2_JCA_2002_9_2_a1/