Unified approach to some geometric results in variational analysis |
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| Authors: | Guoyin Li Kung Fu Ng Xi Yin Zheng |
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| Institution: | a Department of Mathematics, The Chinese University of Hong Kong, Shatin, New Territory, Hong Kong, PR China
b Department of Mathematics, Yunnan University, Kunming 650091, PR China |
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| Abstract: | Based on a study of a minimization problem, we present the following results applicable to possibly nonconvex sets in a Banach space: an approximate projection result, an extended extremal principle, a nonconvex separation theorem, a generalized Bishop-Phelps theorem and a separable point result. The classical result of Dieudonné (on separation of two convex sets in a finite-dimensional space) is also extended to a nonconvex setting. |
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| Keywords: | Abstract subdifferential Outer ?-minimizer Variational analysis The Bishop-Phelps theorem Dieudonné 's separation result |
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