Abstract
In this paper, we consider a linear constraint system with a set constraint. We investigate the Lipschitz-like property of such systems with an explicit set constraint under full perturbations (including the matrix perturbation) and derive some sufficient and necessary conditions for this property. We also make use of some other approaches like outer-subdifferentials and error bounds to characterize such a property. We later apply the obtained results to linear portfolio selection problems with different settings and obtain some sufficient conditions for the parametric feasible set mapping to enjoy the Lipschitz-like property with various stock selection constraints.
| Original language | English |
|---|---|
| Pages (from-to) | 1281-1296 |
| Number of pages | 16 |
| Journal | Journal of Optimization Theory and Applications |
| Volume | 199 |
| Issue number | 3 |
| Early online date | 28 Sept 2023 |
| DOIs | |
| Publication status | Published - Dec 2023 |
| Externally published | Yes |
Bibliographical note
Publisher Copyright:© 2023, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
Funding
The second author was partly supported by a project from the Research Grants Council of Hong Kong (Ref No: 15216518) and a PolyU internal grant (UAF5).
Keywords
- Coderivatives
- Linear portfolio selection
- Linear systems
- Lipschitz-like property
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