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Normal coderivative for multifunctions and implicit function theorems |
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| Authors: | G.M. Lee N.N. Tam |
| Affiliation: | a Department of Applied Mathematics, Pukyong National University, Pusan 608-737, Republic of Korea b Department of Mathematics, Hanoi Pedagogical Institute No. 2, Xuan Hoa, Me Linh, Vinh Phuc, Viet Nam c Institute of Mathematics, Vietnamese Academy of Science and Technology, 18 Hoang Quoc Viet road, 10307 Hanoi, Viet Nam |
| Abstract: | In the framework of the theory of normal coderivative for multifunctions, new implicit function theorems are obtained. The main tools of the proofs are the Ekeland variational principle, a nonsmooth version of Fermat's rule, a sum rule, and the differential estimate for marginal functions established by B.S. Mordukhovich and Y. Shao [B.S. Mordukhovich, Y. Shao, Nonsmooth sequential analysis in Asplund spaces, Trans. Amer. Math. Soc. 348 (1996) 1235-1280]. |
| Keywords: | Multifunction Normal coderivative Metric projection Implicit function theorem Lower semicontinuity Metric regularity Pseudo-Lipschitz property |
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