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Journal of Convex Analysis 09 (2002), No. 2, 327--338
Copyright Heldermann Verlag 2002

Upper Hölder Continuity of Minimal Points

Ewa M. Bednarczuk
Systems Research Institute, Polish Academy of Sciences, Newelska 6, 01-447 Warszawa, Poland

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.

Keywords: Minimal points, Hölder multivalued mappings, parametric vector optimization.

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