Isolated calmness and sharp minima via Hölder Graphical Derivatives
- Authors: Kruger, Alexander , López, Marco , Yang, Xiaoqi , Zhu, Jiangxing
- Date: 2022
- Type: Text , Journal article
- Relation: Set-Valued and Variational Analysis Vol. 30, no. 4 (2022), p. 1423-1441
- Relation: https://purl.org/au-research/grants/arc/DP160100854
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- Description: The paper utilizes Hölder graphical derivatives for characterizing Hölder strong subregularity, isolated calmness and sharp minimum. As applications, we characterize Hölder isolated calmness in linear semi-infinite optimization and Hölder sharp minimizers of some penalty functions for constrained optimization. © 2022, The Author(s).
Holder error bounds and holder calmness with applications to convex semi-infinite optimization
- Authors: Kruger, Alexander , Lopez, Marco , Yang, Xiaoqi , Zhu, Jiangxing
- Date: 2019
- Type: Text , Journal article
- Relation: Set-Valued and Variational Analysis Vol. 27, no. 4 (Dec 2019), p. 995-1023
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- Description: Using techniques of variational analysis, necessary and sufficient subdifferential conditions for Holder 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 Holder 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 Holder calmness modulus of the argmin mapping in the framework of linear programming.