On error bound moduli for locally Lipschitz and regular functions

M. H. Li; K. W. Meng; Xiaoqi Yang

doi:10.1007/s10107-017-1200-1

On error bound moduli for locally Lipschitz and regular functions

M. H. Li, K. W. Meng, Xiaoqi Yang

Research output: Journal article publication › Journal article › Academic research › peer-review

8 Citations (Scopus)

Abstract

We show that the distance from 0 to the outer limiting subdifferential of the support function of the subdifferential set, which is essentially the distance from 0 to the end set of the subdifferential set, is an upper estimate of the local error bound modulus. This upper estimate becomes tight for a convex function under some regularity conditions. We show that the distance from 0 to the outer limiting subdifferential set of a lower (Formula presented.) function is equal to the local error bound modulus.

Original language	English
Pages (from-to)	463-487
Number of pages	25
Journal	Mathematical Programming
DOIs	https://doi.org/10.1007/s10107-017-1200-1
Publication status	Published - 25 Oct 2017

Keywords

End set
Error bound modulus
Locally Lipschitz
Lower $${\mathcal {C}}^1$$C1function
Outer limiting subdifferential
Support function

ASJC Scopus subject areas

Software
Mathematics(all)

More information

10.1007/s10107-017-1200-1

http://hdl.handle.net/10397/80844

Cite this

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AU - Li, M. H.

AU - Meng, K. W.

AU - Yang, Xiaoqi

PY - 2017/10/25

Y1 - 2017/10/25

N2 - We show that the distance from 0 to the outer limiting subdifferential of the support function of the subdifferential set, which is essentially the distance from 0 to the end set of the subdifferential set, is an upper estimate of the local error bound modulus. This upper estimate becomes tight for a convex function under some regularity conditions. We show that the distance from 0 to the outer limiting subdifferential set of a lower (Formula presented.) function is equal to the local error bound modulus.

AB - We show that the distance from 0 to the outer limiting subdifferential of the support function of the subdifferential set, which is essentially the distance from 0 to the end set of the subdifferential set, is an upper estimate of the local error bound modulus. This upper estimate becomes tight for a convex function under some regularity conditions. We show that the distance from 0 to the outer limiting subdifferential set of a lower (Formula presented.) function is equal to the local error bound modulus.

KW - End set

KW - Error bound modulus

KW - Locally Lipschitz

KW - Lower $${\mathcal {C}}^1$$C1function

KW - Outer limiting subdifferential

KW - Support function

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U2 - 10.1007/s10107-017-1200-1

DO - 10.1007/s10107-017-1200-1

M3 - Journal article

SN - 0025-5610

SP - 463

EP - 487

JO - Mathematical Programming

JF - Mathematical Programming

ER -

On error bound moduli for locally Lipschitz and regular functions

Abstract

Keywords

ASJC Scopus subject areas

More information

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