Optimal control of variational inequality with applications to axisymmetric shells

Ján Lovíšek

Aplikace matematiky (1987)

  • Volume: 32, Issue: 6, page 459-479
  • ISSN: 0862-7940

Abstract

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The optimal control problem of variational inequality with applications to axisymmetric shells is discussed. First an existence result for the solution of the optimal control problem is given. Next is presented the formulation of first order necessary conditionas of optimality for the control problem governed by a variational inequality with its coefficients as control variables.

How to cite

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Lovíšek, Ján. "Optimal control of variational inequality with applications to axisymmetric shells." Aplikace matematiky 32.6 (1987): 459-479. <http://eudml.org/doc/15516>.

@article{Lovíšek1987,
abstract = {The optimal control problem of variational inequality with applications to axisymmetric shells is discussed. First an existence result for the solution of the optimal control problem is given. Next is presented the formulation of first order necessary conditionas of optimality for the control problem governed by a variational inequality with its coefficients as control variables.},
author = {Lovíšek, Ján},
journal = {Aplikace matematiky},
keywords = {second invariant of the stress deviator; smooth regularized control problems; optimal shape design; axisymmetric shells; elliptic; linear symmetric operator; first order necessary conditions of optimality; nonsmooth; nonconvex infinite dimensional opimization problem; second invariant of the stress deviator; smooth regularized control problems; optimal shape design; axisymmetric shells; elliptic, linear, symmetric operator; unique solution of a variational inequality; first order necessary conditions of optimality; nonsmooth; nonconvex infinite dimensional opimization problem},
language = {eng},
number = {6},
pages = {459-479},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Optimal control of variational inequality with applications to axisymmetric shells},
url = {http://eudml.org/doc/15516},
volume = {32},
year = {1987},
}

TY - JOUR
AU - Lovíšek, Ján
TI - Optimal control of variational inequality with applications to axisymmetric shells
JO - Aplikace matematiky
PY - 1987
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 32
IS - 6
SP - 459
EP - 479
AB - The optimal control problem of variational inequality with applications to axisymmetric shells is discussed. First an existence result for the solution of the optimal control problem is given. Next is presented the formulation of first order necessary conditionas of optimality for the control problem governed by a variational inequality with its coefficients as control variables.
LA - eng
KW - second invariant of the stress deviator; smooth regularized control problems; optimal shape design; axisymmetric shells; elliptic; linear symmetric operator; first order necessary conditions of optimality; nonsmooth; nonconvex infinite dimensional opimization problem; second invariant of the stress deviator; smooth regularized control problems; optimal shape design; axisymmetric shells; elliptic, linear, symmetric operator; unique solution of a variational inequality; first order necessary conditions of optimality; nonsmooth; nonconvex infinite dimensional opimization problem
UR - http://eudml.org/doc/15516
ER -

References

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  1. R. A. Adams, Sobolev spaces, Academic Press, New York, San Francisco, London 1975. (1975) Zbl0314.46030MR0450957
  2. H. Attouch, Convergence des solutions d'inequations variationnelles avec obstacle, Proceedings of the international meeting on recent methods in nonlinear analysis. Rome, may 1978, ed. by E. De Giorgi - E. Magenes - U. Mosco. (1978) 
  3. V. Barbu, Optimal control of variational inequalities, Pitman Advanced Publishing Program, Boston, London, Melbourne 1984. (1984) Zbl0574.49005MR0742624
  4. I. Boccardo A. Dolcetta, Stabilita delle soluzioni di disequazioni variazionali ellitiche e paraboliche quasi - lineari, Ann. Universeta Ferrara, 24 (1978), 99-111. (1978) 
  5. J. M. Boisserie, Glowinski, Optimization of the thickness law for thin axisymmetric shells, Computers 8. Structures, 8 (1978), 331-343. (1978) Zbl0379.73090
  6. I. Hlaváček, Optimalization of the shape of axisymmetric shells, Aplikace matematiky 28, с. 4, pp. 269-294. MR0710176
  7. J. L. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod Paris, 1969. (1969) Zbl0189.40603MR0259693
  8. F. Mignot, 10.1016/0022-1236(76)90017-3, Journal Functional Analysis. 22 (1976), 130-185. (1976) Zbl0364.49003MR0423155DOI10.1016/0022-1236(76)90017-3
  9. J. Nečas, Les méthodes directes en theorie des équations elliptiques, Academia, Praha, 1967. (1967) MR0227584
  10. J. Nečas I. Hlaváček, Mathematical theory of elastic and elasto-plastic bodies. An introduction, Amsterdam, Elsevier, 1981. (1981) MR0600655
  11. P. D. Panagiotopoulos, Inequality problems in mechanics and applications, Birkhäuser, Boston-Basel-Stuttgart, 1985. (1985) Zbl0579.73014MR0896909
  12. J. P. Yvon, Controle optimal de systémes gouvernes par des inéquations variationnelles, Rapport Laboria, February 1974. (1974) 
  13. O. C. Zienkiewcz, The Finite Element Method in Engineering, Science, McGraw Hill, London, 1984. (1984) 

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