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Peer-reviewedCC BYEvolution Equations and Control Theory

Pointwise boundary observation in geometric optimization problems associated to variational inequalities

  • Livia Betz
  • Cornel Marius Murea
  • Dan Tiba
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Abstract

We discuss optimal design problems governed by variational inequalities with unilateral conditions in the domain and involving pointwise boundary observation. We use penalization techniques in the frame of the Hamiltonian approach to shape/topology optimization problems. For the regularization of the penalized problem, we compute the gradient of the reduced objective via novel adjoint systems. In the purely non-smooth case, approximation and sensitivity analysis results are established with respect to functional variations. In the context of non-smooth PDEs, these allow us to state a primal necessary condition, in the sense that the directional derivative of the reduced objective in feasible directions is nonnegative. Numerical examples, based on gradient-type algorithms, are also included.

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Cite

BibTeXRIS
BibTeX
@article{betz2026pointwise,
  title = {{Pointwise boundary observation in geometric optimization problems associated to variational inequalities}},
  author = {Livia Betz and Cornel Marius Murea and Dan Tiba},
  journal = {Evolution Equations and Control Theory},
  year = {2026},
  month = sep,
  doi = {10.3934/eect.2026095},
  url = {https://hal.science/hal-05733703v1},
  note = {CC BY},
}
RIS
TY  - JOUR
TI  - Pointwise boundary observation in geometric optimization problems associated to variational inequalities
AU  - Livia Betz
AU  - Cornel Marius Murea
AU  - Dan Tiba
PY  - 2026
DA  - 2026/09/01
JO  - Evolution Equations and Control Theory
DO  - 10.3934/eect.2026095
UR  - https://hal.science/hal-05733703v1
AB  - We discuss optimal design problems governed by variational inequalities with unilateral conditions in the domain and involving pointwise boundary observation. We use penalization techniques in the frame of the Hamiltonian approach to shape/topology optimization problems. For the regularization of the penalized problem, we compute the gradient of the reduced objective via novel adjoint systems. In the purely non-smooth case, approximation and sensitivity analysis results are established with respect to functional variations. In the context of non-smooth PDEs, these allow us to state a primal necessary condition, in the sense that the directional derivative of the reduced objective in feasible directions is nonnegative. Numerical examples, based on gradient-type algorithms, are also included.
SN  - 2163-2472
SN  - 2163-2480
ER  -