Journal of Convex Analysis 24 (2017), No. 2, 417--457
Copyright Heldermann Verlag 2017
Directional Hölder Metric Subregularity and Application to Tangent Cones
Huynh Van Ngai
Dept. of Mathematics, University of Quy Nhon, 170 An Duong Vuong, Quy Nhon, Vietnam
ngaivn@yahoo.com
Nguyen Huu Tron
Dept. of Mathematics, University of Quy Nhon, 170 An Duong Vuong, Quy Nhon, Vietnam
nguyenhuutron@qnu.edu.vn
Phan Nhat Tinh
Dept. of Mathematics, Hue University of Science, 77 Nguyen Hue, Hue, Vietnam
pntinh@yahoo.com
We study directional versions of the Hölderian/Lipschitzian metric subregularity of multifunctions. Firstly, we establish variational characterizations of the Hölderian/Lipschitzian directional metric subregularity by means of the strong slopes and next of mixed tangency-coderivative objects. By product, we give second-order conditions for the directional Lipschitzian metric subregularity and for the directional metric subregularity of demi order. An application of the directional metric subregularity to study the tangent cone is discussed.
Keywords: Error bound, generalized equation, metric subregularity, Hölder metric subregularity, directional Hölder metric subregularity, coderivative.
MSC: 49J52, 49J53, 58C06, 47H04, 54C60, 90C30
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