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Directional H\"older metric subregularity and application to tangent cones

Huynh Van Ngai(ngaivn***at***yahoo.com)
Nguyen Huu Tron(nguyenhuutron***at***qnu.edu.vn)
Phan Nhat Tinh(pntinh***at***yahoo.com)

Abstract: In this work, we study directional versions of the H\"olderian/Lipschitzian metric subregularity of multifunctions. Firstly, we establish variational characterizations of the H\"olderian/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, H\"older Metric subregularity, Directional H\"older metric subregularity, Coderivative.

Category 1: Convex and Nonsmooth Optimization

Citation:

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Entry Submitted: 11/04/2014
Entry Accepted: 11/04/2014
Entry Last Modified: 11/04/2014

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