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.
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Acknowledgements
The authors are grateful to the anonymous reviewers for their careful reading and valuable suggestions. The authors would like to thank Dr. Li Minghua for his useful discussions during the development of this article. 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).
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Communicated by René Henrion.
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Yao, W., Yang, X. Lipschitz-Like Property for Linear Constraint Systems. J Optim Theory Appl 199, 1281–1296 (2023). https://doi.org/10.1007/s10957-023-02300-6
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DOI: https://doi.org/10.1007/s10957-023-02300-6