
Journal of Convex Analysis 24 (2017), No. 2, 417457 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 tangencycoderivative objects. By product, we give secondorder 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 [ Fulltextpdf (283 KB)] for subscribers only. 