nite - dimensional image . Necessary conditions for unilateral constraints

In Ref.1, extremum problems having in nite-dimensional image have been considered and some preliminary properties have been established. Here we carry on the investigation of such problems and study an optimality condition for the case of unilateral constraints, which partially extends the results of [2,3] to the present type of problems. This is done by associating to the feasible set a special multifunction. It turns out that the classic Lagrangian multitplier functions can be factorized into a constant term and a variable one; the former is the gradient of a separating hyperplane as introduced in [2,3]; the latter plays the role of selector of the above multifunction. Finally, the need of enlarging the class of Lagrangian multiplier functions is discussed.