Singular perturbations in optimal control problem with application to nonlinear structural analysis

Ján Lovíšek

Applications of Mathematics (1996)

  • Volume: 41, Issue: 4, page 299-320
  • ISSN: 0862-7940

Abstract

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This paper concerns an optimal control problem of elliptic singular perturbations in variational inequalities (with controls appearing in coefficients, right hand sides and convex sets of states as well). The existence of an optimal control is verified. Applications to the optimal control of an elasto-plastic plate with a small rigidity and with an obstacle are presented. For elasto-plastic plates with a moving part of the boundary a primal finite element model is applied and a convergence result is obtained.

How to cite

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Lovíšek, Ján. "Singular perturbations in optimal control problem with application to nonlinear structural analysis." Applications of Mathematics 41.4 (1996): 299-320. <http://eudml.org/doc/32952>.

@article{Lovíšek1996,
abstract = {This paper concerns an optimal control problem of elliptic singular perturbations in variational inequalities (with controls appearing in coefficients, right hand sides and convex sets of states as well). The existence of an optimal control is verified. Applications to the optimal control of an elasto-plastic plate with a small rigidity and with an obstacle are presented. For elasto-plastic plates with a moving part of the boundary a primal finite element model is applied and a convergence result is obtained.},
author = {Lovíšek, Ján},
journal = {Applications of Mathematics},
keywords = {optimal control problem; singular perturbations in variational inequalities; convex set; elasto-plastic plate; small rigidity; obstacle; optimal control of variational inequalities; elasto-plastic plate; singular perturbation},
language = {eng},
number = {4},
pages = {299-320},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Singular perturbations in optimal control problem with application to nonlinear structural analysis},
url = {http://eudml.org/doc/32952},
volume = {41},
year = {1996},
}

TY - JOUR
AU - Lovíšek, Ján
TI - Singular perturbations in optimal control problem with application to nonlinear structural analysis
JO - Applications of Mathematics
PY - 1996
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 41
IS - 4
SP - 299
EP - 320
AB - This paper concerns an optimal control problem of elliptic singular perturbations in variational inequalities (with controls appearing in coefficients, right hand sides and convex sets of states as well). The existence of an optimal control is verified. Applications to the optimal control of an elasto-plastic plate with a small rigidity and with an obstacle are presented. For elasto-plastic plates with a moving part of the boundary a primal finite element model is applied and a convergence result is obtained.
LA - eng
KW - optimal control problem; singular perturbations in variational inequalities; convex set; elasto-plastic plate; small rigidity; obstacle; optimal control of variational inequalities; elasto-plastic plate; singular perturbation
UR - http://eudml.org/doc/32952
ER -

References

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  10. 10.1007/BFb0060528, Springer Verlag, Berlin, 1973. (1973) MR0600331DOI10.1007/BFb0060528
  11. Singular perturbation and singular layers in variational inequalities, Contribution to Nonlinear Analysis, E.H. Zarantonello (ed.), Acad. Press, New York, 1971. (1971) MR0390457
  12. 10.1137/0322028, SIAM J. Control Optimiz. 22 (1984), 466–476. (1984) MR0739836DOI10.1137/0322028
  13. 10.1016/0001-8708(69)90009-7, Advances of Math. 3 (1969), 510–585. (1969) Zbl0192.49101MR0298508DOI10.1016/0001-8708(69)90009-7
  14. Obstacle Problems in Mathematical Physics, North Holland Math. Studies, Amsterdam, 1986. (1986) MR0880369

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