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PreprintCC BY 4.0arXiv

First-order approximations of multifunctions defined implicitly by "split" feasibility problems with applications to optimization

  • Amos Uderzo
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Abstract

In the present paper, a study is made of first-order differential properties of certain multifunctions, which are defined as a solution map associated with a family of parameterized ``split" feasibility problems. The latter are a class of convex feasibility problems, whose specific structure makes them suitable for well-established applications in several areas of engineering and systems biology. As a result, inner and outer approximations of the graphical (contingent) derivative of the solution map are provided, which are expressed in terms of derivatives of the problem data. As an application, a perspective is also discussed for employing some of these achievements in the formulation of optimality conditions for mathematical programs with ``split" feasibility constraints.

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Cite

BibTeXRIS
BibTeX
@misc{uderzo2026firstorder,
  title = {{First-order approximations of multifunctions defined implicitly by "split" feasibility problems with applications to optimization}},
  author = {Amos Uderzo},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2608.28319},
  eprint = {2608.28319},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.28319},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - First-order approximations of multifunctions defined implicitly by "split" feasibility problems with applications to optimization
AU  - Amos Uderzo
PY  - 2026
DA  - 2026/08/28
PB  - arXiv
DO  - 10.48550/arxiv.2608.28319
UR  - https://arxiv.org/abs/2608.28319
AB  - In the present paper, a study is made of first-order differential properties of certain multifunctions, which are defined as a solution map associated with a family of parameterized ``split" feasibility problems. The latter are a class of convex feasibility problems, whose specific structure makes them suitable for well-established applications in several areas of engineering and systems biology. As a result, inner and outer approximations of the graphical (contingent) derivative of the solution map are provided, which are expressed in terms of derivatives of the problem data. As an application, a perspective is also discussed for employing some of these achievements in the formulation of optimality conditions for mathematical programs with ``split" feasibility constraints.
ER  -