Éditeur(s) : HAL CCSD Society for Industrial and Applied Mathematics
Résumé : International audience
We discuss the control of distributed systems with incomplete data following the notion of no-regret control (or, equivalently, Pareto control) used by Lions in [C. R. Acad. Sci. Paris Ser. I Math., 302 (1986), pp. 223-227] and [C. R. Acad. Sci. Paris Ser. I Math., 302 (1992), pp. 1253-1257]. We associate with the no-regret control a sequence of low-regret controls defined by a quadratic perturbation previously used by Nakoulima, Omrane, and Velin in [C. R. Acad. Sci. Paris Ser. I Math., 330 (2000), pp. 801-806]. In the first part, we prove that the perturbed system corresponds to a sequence of standard control problems and converges to the no-regret (or Pareto) control for which we obtain a singular optimality system. We give also some applications. In the second part, we show how the method can be extended to the evolution case. Equations of parabolic type, Petrowsky type, or hyperbolic type are considered.
ISSN: 0363-0129

hal-00764259
https://hal.univ-antilles.fr/hal-00764259
https://hal.univ-antilles.fr/hal-00764259/document
https://hal.univ-antilles.fr/hal-00764259/file/38018.pdf
DOI : 10.1137/S0363012900380188

Éditeur(s) : HAL CCSD
Résumé : International audience
We deal with a perturbed version of a Hummel-Seebeck type method to approximate a solution of variational inclusions of the form : 0 ∈ Φ(z) + F(z) where Φ is a single-valued function twice continuously Fréchet differentiable and F is a set-valued map from Rn to the closed subsets of Rn. This framework is convenient to treat in a unified way standard sequential quadratic programming, its stabilized version, sequential quadratically constrained quadratic programming, and linearly constrained Lagrangian methods (see [1]). We obtain, thanks to some semistability and another property (which is close to the hemistability) of the solution z ̄ of the previous inclusion, the local existence of a sequence that is superquadratically or cubically convergent.
ISSN: 2518-3680

hal-01630560
https://hal.archives-ouvertes.fr/hal-01630560
DOI : 10.22606