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PreprintCC BY 4.0arXiv

Stability Analysis of Generalized Multi-Source Weber Problems

  • N. H. Hai
  • V. S. T. Long
  • N. M. Nam
  • N. D. Yen
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Abstract

This paper presents a stability analysis of the generalized multi-source Weber problems under the influence of data perturbation within the framework of the Minkowski function. First, we establish explicit Lipschitz constants for the objective functions and optimal value functions. Then, we prove several properties of the global optimal solution sets. Furthermore, we provide sufficient conditions for the upper semicontinuity of global solution mappings and the inner semicontinuity of local solution mappings. Three illustrative examples are constructed. Our results give indirect answers to several open questions regarding the stability of local optimal solution mappings of the optimization problems discussed.

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Cite

BibTeXRIS
BibTeX
@misc{hai2026stability,
  title = {{Stability Analysis of Generalized Multi-Source Weber Problems}},
  author = {N. H. Hai and V. S. T. Long and N. M. Nam and N. D. Yen},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.16703},
  eprint = {2609.16703},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.16703},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Stability Analysis of Generalized Multi-Source Weber Problems
AU  - N. H. Hai
AU  - V. S. T. Long
AU  - N. M. Nam
AU  - N. D. Yen
PY  - 2026
DA  - 2026/09/15
PB  - arXiv
DO  - 10.48550/arxiv.2609.16703
UR  - https://arxiv.org/abs/2609.16703
AB  - This paper presents a stability analysis of the generalized multi-source Weber problems under the influence of data perturbation within the framework of the Minkowski function. First, we establish explicit Lipschitz constants for the objective functions and optimal value functions. Then, we prove several properties of the global optimal solution sets. Furthermore, we provide sufficient conditions for the upper semicontinuity of global solution mappings and the inner semicontinuity of local solution mappings. Three illustrative examples are constructed. Our results give indirect answers to several open questions regarding the stability of local optimal solution mappings of the optimization problems discussed.
ER  -