Optimal control problems for variational inequalities with controls in coefficients and in unilateral constraints

Igor Bock; Ján Lovíšek

Aplikace matematiky (1987)

  • Volume: 32, Issue: 4, page 301-314
  • ISSN: 0862-7940

Abstract

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We deal with an optimal control problem for variational inequalities, where the monotone operators as well as the convex sets of possible states depend on the control parameter. The existence theorem for the optimal control will be applied to the optimal design problems for an elasto-plastic beam and an elastic plate, where a variable thickness appears as a control variable.

How to cite

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Bock, Igor, and Lovíšek, Ján. "Optimal control problems for variational inequalities with controls in coefficients and in unilateral constraints." Aplikace matematiky 32.4 (1987): 301-314. <http://eudml.org/doc/15502>.

@article{Bock1987,
abstract = {We deal with an optimal control problem for variational inequalities, where the monotone operators as well as the convex sets of possible states depend on the control parameter. The existence theorem for the optimal control will be applied to the optimal design problems for an elasto-plastic beam and an elastic plate, where a variable thickness appears as a control variable.},
author = {Bock, Igor, Lovíšek, Ján},
journal = {Aplikace matematiky},
keywords = {optimal control; variational inequalities; optimal design; elasto-plastic beam; elastic plate; obstacle; convex set; thickness-function; optimal control; variational inequalities; optimal design; elasto-plastic beam; elastic plate; obstacle},
language = {eng},
number = {4},
pages = {301-314},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Optimal control problems for variational inequalities with controls in coefficients and in unilateral constraints},
url = {http://eudml.org/doc/15502},
volume = {32},
year = {1987},
}

TY - JOUR
AU - Bock, Igor
AU - Lovíšek, Ján
TI - Optimal control problems for variational inequalities with controls in coefficients and in unilateral constraints
JO - Aplikace matematiky
PY - 1987
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 32
IS - 4
SP - 301
EP - 314
AB - We deal with an optimal control problem for variational inequalities, where the monotone operators as well as the convex sets of possible states depend on the control parameter. The existence theorem for the optimal control will be applied to the optimal design problems for an elasto-plastic beam and an elastic plate, where a variable thickness appears as a control variable.
LA - eng
KW - optimal control; variational inequalities; optimal design; elasto-plastic beam; elastic plate; obstacle; convex set; thickness-function; optimal control; variational inequalities; optimal design; elasto-plastic beam; elastic plate; obstacle
UR - http://eudml.org/doc/15502
ER -

References

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  1. I. Bock J. Lovíšek, An optimal control problem for an elliptic variational inequality, Math Slovaca 33, 1983, No. 1, 23-28. (1983) Zbl0517.49005MR0689273
  2. M. Chipot, Variational inequalities and flow in porous media, Springer Verlag 1984. (1984) Zbl0544.76095MR0747637
  3. I. Hlaváček I. Bock J. Lovíšek, 10.1007/BF01442173, Appl. Math. Optimization 11, 1984, 111-143. (1984) Zbl0553.73082MR0743922DOI10.1007/BF01442173
  4. I. Hlaváček I. Bock J. Lovíšek, 10.1007/BF01442202, Appl. Math. Optimization 13, 1985, 117-136. (1985) Zbl0582.73081MR0794174DOI10.1007/BF01442202
  5. D. Kinderlehrer G. Stampacchia, An introduction to variational inequalities and their applications, Academic Press 1980. (1980) Zbl0457.35001MR0567696
  6. A. Langenbach, Monotone Potentialoperatoren in Theorie und Anwendung, VEB Deutsche Verlag der Wissenschaften, Berlin 1976. (1976) Zbl0387.47037MR0495530
  7. J. L. Lions, Quelques méthodes de résolution děs problèmes aux limites non linéaires, Dunod, Paris 1969. (1969) Zbl0189.40603MR0259693
  8. U. Mosco, Convergence of convex sets and of solutions of variational inequalities, Advances of Math. 3, 1969,510-585. (1969) Zbl0192.49101MR0298508
  9. F. Murat, L’injection du cone positif de H - 1 dans W - 1 , 2 est compact pour tout q < 2, J. Math. Pures Appl. 60, 1981, 309-321. (1981) MR0633007

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