Complete characterizations of local weak sharp minima with applications to semi-infinite optimization and complementarity |
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Authors: | Jinchuan Zhou Naihua Xiu |
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Institution: | a Department of Mathematics, School of Science, Shandong University of Technology, Zibo 255049, PR Chinab Department of Mathematics, Wayne State University, Detroit, MI 48202, USAc Department of Mathematics, School of Science, Beijing Jiaotong University, Beijing 100044, PR China |
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Abstract: | In this paper, we identify a favorable class of nonsmooth functions for which local weak sharp minima can be completely characterized in terms of normal cones and subdifferentials, or tangent cones and subderivatives, or their mixture in finite-dimensional spaces. The results obtained not only extend previous ones in the literature, but also allow us to provide new types of criteria for local weak sharpness. Applications of the developed theory are given to semi-infinite programming and to a new class of semi-infinite complementarity problems. |
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Keywords: | 49J52 65K10 90C26 |
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