Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

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

Keywords

  • Error bound
  • generalized equation
  • metric subregularity
  • Hölder metric subregularity
  • directional Hölder metric subregularity
  • coderivative

Mathematics Subject Classification

49J52, 49J53, 58C06, 47H04, 54C60, 90C30

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Suggested citation

H. V. Ngai, N. H. Tron, P. N. Tinh. “Directional Hölder Metric Subregularity and Application to Tangent Cones.” Journal of Convex Analysis 24 (2017), No. 2, 417–457. https://doi.org/10.68381/jca24028

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