Hölder Error Bounds and Hölder Calmness with Applications to Convex Semi-infinite Optimization

Alexander Y. Kruger; Marco A. López; Xiaoqi Yang; Jiangxing Zhu

doi:10.1007/s11228-019-0504-0

Hölder Error Bounds and Hölder Calmness with Applications to Convex Semi-infinite Optimization

Alexander Y. Kruger, Marco A. López, Xiaoqi Yang, Jiangxing Zhu

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

17 Citations (Scopus)

Abstract

Using techniques of variational analysis, necessary and sufficient subdifferential conditions for Hölder error bounds are investigated and some new estimates for the corresponding modulus are obtained. As an application, we consider the setting of convex semi-infinite optimization and give a characterization of the Hölder calmness of the argmin mapping in terms of the level set mapping (with respect to the objective function) and a special supremum function. We also estimate the Hölder calmness modulus of the argmin mapping in the framework of linear programming.

Original language	English
Pages (from-to)	995-1023
Number of pages	29
Journal	Set-Valued and Variational Analysis
Volume	27
Issue number	4
DOIs	https://doi.org/10.1007/s11228-019-0504-0
Publication status	Published - Dec 2019

Keywords

Convex programming
Hölder calmness
Hölder error bounds
Semi-infinite programming

ASJC Scopus subject areas

Analysis
Statistics and Probability
Numerical Analysis
Geometry and Topology
Applied Mathematics

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10.1007/s11228-019-0504-0

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abstract = "Using techniques of variational analysis, necessary and sufficient subdifferential conditions for H{\"o}lder error bounds are investigated and some new estimates for the corresponding modulus are obtained. As an application, we consider the setting of convex semi-infinite optimization and give a characterization of the H{\"o}lder calmness of the argmin mapping in terms of the level set mapping (with respect to the objective function) and a special supremum function. We also estimate the H{\"o}lder calmness modulus of the argmin mapping in the framework of linear programming.",

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AU - Kruger, Alexander Y.

AU - López, Marco A.

AU - Yang, Xiaoqi

AU - Zhu, Jiangxing

PY - 2019/12

Y1 - 2019/12

N2 - Using techniques of variational analysis, necessary and sufficient subdifferential conditions for Hölder error bounds are investigated and some new estimates for the corresponding modulus are obtained. As an application, we consider the setting of convex semi-infinite optimization and give a characterization of the Hölder calmness of the argmin mapping in terms of the level set mapping (with respect to the objective function) and a special supremum function. We also estimate the Hölder calmness modulus of the argmin mapping in the framework of linear programming.

AB - Using techniques of variational analysis, necessary and sufficient subdifferential conditions for Hölder error bounds are investigated and some new estimates for the corresponding modulus are obtained. As an application, we consider the setting of convex semi-infinite optimization and give a characterization of the Hölder calmness of the argmin mapping in terms of the level set mapping (with respect to the objective function) and a special supremum function. We also estimate the Hölder calmness modulus of the argmin mapping in the framework of linear programming.

KW - Convex programming

KW - Hölder calmness

KW - Hölder error bounds

KW - Semi-infinite programming

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VL - 27

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JO - Set-Valued and Variational Analysis

JF - Set-Valued and Variational Analysis

IS - 4

ER -

Hölder Error Bounds and Hölder Calmness with Applications to Convex Semi-infinite Optimization

Abstract

Keywords

ASJC Scopus subject areas

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