Fréchet and normal coderivatives of implicit multifunctions

Abstract

This article analyses and develops furthermore the existing upper and lower estimates for the Fréchet and normal coderivatives of implicit multifunctions. Various counterexamples and examples are given. The effect of right-hand side perturbations is discussed in detail.

Keywords:

• implicit multifunction
• Fréchet coderivative
• normal coderivative
• upper estimate
• lower estimate

AMS Subject Classifications::

• 49J53
• 26B10

Acknowledgements

G.M. Lee was supported by the Korea Science and Engineering Foundation (KOSEF) NRL Program grant funded by the Korea government (MEST) (No. ROA-2008-000-20010-0). N.D. Yen was supported by the National Foundation for Science & Technology Development (Vietnam). The authors thank Dr Nguyen Quang Huy for providing a copy of the Master thesis 11 which was written under his guidance. We would like to thank Nguyen Huy Chieu, Nguyen Thi Quynh Trang, and the referees for helpful comments.