Lipschitz upper semicontinuity of linear inequality systems under full perturbations
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866909601433124864 |
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| author | Camacho, Jesús Cánovas, María Josefa Gfrerer, Helmut Parra, Juan |
| author_facet | Camacho, Jesús Cánovas, María Josefa Gfrerer, Helmut Parra, Juan |
| contents | The present paper is focused on the computation of the Lipschitz upper semicontinuity modulus of the feasible set mapping in the context of fully perturbed linear inequality systems; i.e., where all coefficients are allowed to be perturbed. The direct antecedent comes from the framework of right-hand side (RHS, for short) perturbations. The difference between both parametric contexts, full vs RHS perturbations, is emphasized. In particular, the polyhedral structure of the graph of the feasible set mapping in the latter framework enables us to apply classical results as those of Hoffman [A. J. HOFFMAN, J. Res. Natl. Bur. Stand. 49 (1952), pp. 263--265] and Robinson [S. M. ROBINSON, Math. Progr. Study 14 (1981), pp. 206--214]. In contrast, the graph of the feasible set mapping under full perturbations is no longer polyhedral (not even convex). This fact requires ad hoc techniques to analyze the Lipschitz upper semicontinuity property and its corresponding modulus. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_02575 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Lipschitz upper semicontinuity of linear inequality systems under full perturbations Camacho, Jesús Cánovas, María Josefa Gfrerer, Helmut Parra, Juan Optimization and Control 90C31, 49J53, 49K40, 90C05 The present paper is focused on the computation of the Lipschitz upper semicontinuity modulus of the feasible set mapping in the context of fully perturbed linear inequality systems; i.e., where all coefficients are allowed to be perturbed. The direct antecedent comes from the framework of right-hand side (RHS, for short) perturbations. The difference between both parametric contexts, full vs RHS perturbations, is emphasized. In particular, the polyhedral structure of the graph of the feasible set mapping in the latter framework enables us to apply classical results as those of Hoffman [A. J. HOFFMAN, J. Res. Natl. Bur. Stand. 49 (1952), pp. 263--265] and Robinson [S. M. ROBINSON, Math. Progr. Study 14 (1981), pp. 206--214]. In contrast, the graph of the feasible set mapping under full perturbations is no longer polyhedral (not even convex). This fact requires ad hoc techniques to analyze the Lipschitz upper semicontinuity property and its corresponding modulus. |
| title | Lipschitz upper semicontinuity of linear inequality systems under full perturbations |
| topic | Optimization and Control 90C31, 49J53, 49K40, 90C05 |
| url | https://arxiv.org/abs/2505.02575 |