Point-based sufficient conditions for metric regularity of implicit multifunctions. (English) Zbl 1156.49014
Summary: We obtain some point-based sufficient conditions for the metric regularity in Robinson’s sense of implicit multifunctions in a finite-dimensional setting. The new implicit function theorem (which is very different from the preceding results of Yu. S. Ledyaev and Q. J. Zhu [Set-Valued Anal. 7, No. 3, 209–238 (1999; Zbl 0952.49017)], H. V. Ngai and M. Théra [Set-Valued Anal. 12, No. 1–2, 195–223 (2004; Zbl 1058.49017)], G. M. Lee, N. N. Tam and N. D. Yen [J. Math. Anal. Appl. 338, No. 1, 11–22 (2008; Zbl 1140.49013)] can be used for analyzing parametric constraint systems as well as parametric variational systems. Our main tools are the concept of normal coderivative due to Mordukhovich and the corresponding theory of generalized differentiation.
MSC:
| 49J52 | Nonsmooth analysis |
| 49J53 | Set-valued and variational analysis |
| 49N60 | Regularity of solutions in optimal control |
Keywords:
implicit multifunction; local metric regularity in Robinson’s sense; point-based sufficient condition; normal coderivative; robustnessReferences:
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