Locally Lipschitzian set-valued maps and generalized extremal problems with inclusion constraints (Q1057477)

Some properties of locally Lipschitzian multifunctions \(F:\quad X\to Y\) with nonempty, compact and convex values are presented in terms of the support function and the distance function between the point (x,y) and the graph of F. X, Y are two Hilbert spaces. Next, by using the adjoint multifunction (in sense of Pshenichnyj) an interior mapping theorem (for Y to be finite-dimensional) is proved. At the end, a multicriterial optimization problem for a functional S:X\(\to E\) (E is a Hilbert space and optimality is understood with respect to the order defined by some non-trivial cone) on the null-set of the multifunction F is considered, and a necessary optimality condition is obtained by using Ekeland's variational principle. Shoppy redaction and a lot of misprints characterize this paper.