Openness results for parametric set-valued mappings in Asplund spaces. (English) Zbl 1346.90812

Yang, Ming-Ge; Xu, Yi-Fan

Optim. Lett. 8, No. 8, 2227-2243 (2014).

Authors’ abstract: In this paper, we first prove a lemma about the lower semicontinuity of the distance function

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in infinite dimensional spaces, which is crucial to openness results hereafter. Then we obtain some openness results in terms of Fréchet coderivatives for parametric set-valued mappings in Asplund spaces under mild conditions. The results of the paper generalize several corresponding results in the recent literature. Finally, we give two examples to illustrate our openness results.

Reviewer: Paulo Mbunga (Kiel)

MSC:

90C48	Programming in abstract spaces
90C31	Sensitivity, stability, parametric optimization

Keywords:

openness; Fréchet coderivative; Fréchet subdifferential; Fréchet differentiable; proximinal set

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