An instantaneous semi-Lagrangian approach for boundary control of a melting problem

Youness Mezzan; Moulay Hicham Tber

Applications of Mathematics (2021)

  • Volume: 66, Issue: 5, page 725-744
  • ISSN: 0862-7940

Abstract

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In this paper, a sub-optimal boundary control strategy for a free boundary problem is investigated. The model is described by a non-smooth convection-diffusion equation. The control problem is addressed by an instantaneous strategy based on the characteristics method. The resulting time independent control problems are formulated as function space optimization problems with complementarity constraints. At each time step, the existence of an optimal solution is proved and first-order optimality conditions with regular Lagrange multipliers are derived for a penalized-regularized version. The performance of the overall approach is illustrated by numerical examples.

How to cite

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Mezzan, Youness, and Tber, Moulay Hicham. "An instantaneous semi-Lagrangian approach for boundary control of a melting problem." Applications of Mathematics 66.5 (2021): 725-744. <http://eudml.org/doc/297487>.

@article{Mezzan2021,
abstract = {In this paper, a sub-optimal boundary control strategy for a free boundary problem is investigated. The model is described by a non-smooth convection-diffusion equation. The control problem is addressed by an instantaneous strategy based on the characteristics method. The resulting time independent control problems are formulated as function space optimization problems with complementarity constraints. At each time step, the existence of an optimal solution is proved and first-order optimality conditions with regular Lagrange multipliers are derived for a penalized-regularized version. The performance of the overall approach is illustrated by numerical examples.},
author = {Mezzan, Youness, Tber, Moulay Hicham},
journal = {Applications of Mathematics},
keywords = {free boundary problem; sub-optimal boundary control; characteristics method; complementarity constraint; penalization-regularization},
language = {eng},
number = {5},
pages = {725-744},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {An instantaneous semi-Lagrangian approach for boundary control of a melting problem},
url = {http://eudml.org/doc/297487},
volume = {66},
year = {2021},
}

TY - JOUR
AU - Mezzan, Youness
AU - Tber, Moulay Hicham
TI - An instantaneous semi-Lagrangian approach for boundary control of a melting problem
JO - Applications of Mathematics
PY - 2021
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 66
IS - 5
SP - 725
EP - 744
AB - In this paper, a sub-optimal boundary control strategy for a free boundary problem is investigated. The model is described by a non-smooth convection-diffusion equation. The control problem is addressed by an instantaneous strategy based on the characteristics method. The resulting time independent control problems are formulated as function space optimization problems with complementarity constraints. At each time step, the existence of an optimal solution is proved and first-order optimality conditions with regular Lagrange multipliers are derived for a penalized-regularized version. The performance of the overall approach is illustrated by numerical examples.
LA - eng
KW - free boundary problem; sub-optimal boundary control; characteristics method; complementarity constraint; penalization-regularization
UR - http://eudml.org/doc/297487
ER -

References

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