On optimal control problems connected with eigenvalue variational inequalities

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 fbr 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 (C) 2001 John Wiley & Sons, Ltd.