Stability of error bounds for semi-infinite convex constraint systems
- Authors: Van Ngai, Huynh , Kruger, Alexander , Théra, Michel
- Date: 2010
- Type: Text , Journal article
- Relation: SIAM Journal on Optimization Vol. 20, no. 4 (2010), p. 2080-2096
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- Description: In this paper, we are concerned with the stability of the error bounds for semi-infinite convex constraint systems. Roughly speaking, the error bound of a system of inequalities is said to be stable if all its "small" perturbations admit a (local or global) error bound. We first establish subdifferential characterizations of the stability of error bounds for semi-infinite systems of convex inequalities. By applying these characterizations, we extend some results established by Azé and Corvellec [SIAM J. Optim., 12 (2002), pp. 913-927] on the sensitivity analysis of Hoffman constants to semi-infinite linear constraint systems. Copyright © 2010, Society for Industrial and Applied Mathematics.
Error bounds : Necessary and sufficient conditions
- Authors: Fabian, Marian , Henrion, René , Kruger, Alexander , Outrata, Jiri
- Date: 2010
- Type: Text , Journal article
- Relation: Set-Valued and Variational Analysis Vol. 18, no. 2 (2010), p. 121-149
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- Description: The paper presents a general classification scheme of necessary and sufficient criteria for the error bound property incorporating the existing conditions. Several derivative-like objects both from the primal as well as from the dual space are used to characterize the error bound property of extended-real-valued functions on a Banach space. © 2010 Springer Science+Business Media B.V.
Error bounds and metric subregularity
- Authors: Kruger, Alexander
- Date: 2015
- Type: Text , Journal article
- Relation: Optimization Vol. 64, no. 1 (2015), p. 49-79
- Relation: http://purl.org/au-research/grants/arc/DP110102011
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- Description: Necessary and sufficient criteria for metric subregularity (or calmness) of set-valued mappings between general metric or Banach spaces are treated in the framework of the theory of error bounds for a special family of extended real-valued functions of two variables. A classification scheme for the general error bound and metric subregularity criteria is presented. The criteria are formulated in terms of several kinds of primal and subdifferential slopes.
Error bounds for vector-valued functions : Necessary and sufficient conditions
- Authors: Bednarczuk, Ewa , Kruger, Alexander
- Date: 2012
- Type: Text , Journal article
- Relation: Nonlinear Analysis, Theory, Methods and Applications Vol. 75, no. 3 (2012), p. 1124-1140
- Relation: http://purl.org/au-research/grants/arc/DP110102011
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- Description: In this paper, we attempt to extend the definition and existing local error bound criteria to vector-valued functions, or more generally, to functions taking values in a normed linear space. Some new derivative-like objects (slopes and subdifferentials) are introduced and a general classification scheme of error bound criteria is presented.
- Description: In this paper, we attempt to extend the definition and existing local error bound criteria to vector-valued functions, or more generally, to functions taking values in a normed linear space. Some new derivative-like objects (slopes and subdifferentials) are introduced and a general classification scheme of error bound criteria is presented. © 2011 Elsevier Ltd. All rights reserved.
Slopes of multifunctions and extensions of metric regularity
- Authors: Ngai, Huynh Van , Kruger, Alexander , Thera, Michel
- Date: 2012
- Type: Text , Journal article
- Relation: Vietnam Journal of Mathematics (Tạp chí toán học) Vol. 40, no. 2/3 (2012), p. 355-369
- Relation: http://purl.org/au-research/grants/arc/DP110102011
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- Description: This article aims to demonstrate how the definitions of slopes can be extended to multi-valued mappings between metric spaces and applied for characterizing metric regularity. Several kinds of local and nonlocal slopes are defined and several metric regularity properties for set-valued mappings between metric spaces are investigated.
Stability of error bounds for convex constraints systems in Banach spaces
- Authors: Thera, Michel , Van Ngai, Huynh , Kruger, Alexander
- Date: 2010
- Type: Text , Journal article
- Relation: SIAM Journal on Optimization Vol. 20, no. 6 (2010), p. 3280-3296
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- Description: This paper studies stability of error bounds for convex constraints in Banach spaces. We show that certain known sufficient conditions for local and global error bounds actually ensure error bounds for the family of functions being in a sense small perturbations of the given one. A single inequality as well as semi-infinite constraint systems are considered.
- Description: C1
Error bounds and Hölder metric subregularity
- Authors: Kruger, Alexander
- Date: 2015
- Type: Text , Journal article
- Relation: Set-Valued and Variational Analysis Vol. 23, no. 4 (2015), p. 705-736
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- Description: The Holder setting of the metric subregularity property of set-valued mappings between general metric or Banach/Asplund spaces is investigated in the framework of the theory of error bounds for extended real-valued functions of two variables. A classification scheme for the general Holder metric subregularity criteria is presented. The criteria are formulated in terms of several kinds of primal and subdifferential slopes.