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

Aplikace matematiky (1987)

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

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topBock, 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

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