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Normal coderivative for multifunctions and implicit function theorems |
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| Authors: | GM Lee NN Tam |
| Institution: | 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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