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On optimal control problems connected with eigenvalue variational inequalities
Author(s) -
Bock Igor
Publication year - 2001
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.236
Subject(s) - mathematics , eigenvalues and eigenvectors , variational inequality , convergence (economics) , variable (mathematics) , operator (biology) , optimal control , regular polygon , optimization problem , convex optimization , mathematical analysis , mathematical optimization , geometry , biochemistry , chemistry , physics , repressor , quantum mechanics , transcription factor , economics , gene , economic growth
The eigenvalue optimization problem for a variational inequality over the convex cone is to be dealt with. The control variable appears in the operator of the unilateral problem. The existence theorem for the maximum first eigenvalue optimization problem is stated and verified. The necessary optimality condition is derived. The applications to the optimal design of unilaterally supported beams and plates are presented. The variable thickness of a construction plays the role of a design variable. The convergence of the finite elements approximation is proved. Copyright © 2001 John Wiley & Sons, Ltd.