On optimal control problems connected with eigenvalue variational inequalities (Q2747415)

The author derives a necessary optimality condition for a control problem related to the first eigenvalue of a class of unilateral elliptic problems. This interesting result can be applied to optimal design problems. In the paper, the necessary condition is applied to unilaterally supported beams and plates. In the last section, the convergence of a finite element approximation is proved. Moreover, the author gives an interesting characterization of the first eigenvalue as the maximal value of a functional different from the Rayleigh quotient (Theorem 2.2). The proof of the necessary condition is based on a result for the eigenvalue problem for variational inequalities in convex cones (Miersemann, 1975), on compactness properties of the involved operators and on a theorem concerning differentiability of a functional defined as an infimum over a compact set (Zolesio, 1981).