Abstract
In [1], extremum problems having an infinite-dimensional image were considered and some preliminary properties were established. In this article, an optimality condition of such problems is investigated for the case of unilateral constraints, which partially extends the results of [2, 3]. This is done by associating a special multifunction with the feasible set of solutions. It turns out that any classic Lagrangian multitplier functions can be factorized into a constant term and a variable one; the former term is the gradient of the separating hyperplane introduced in [2, 3], and the latter one plays the role of the selector of the above-mentioned multifunction. Finally, the need of enlarging the class of Lagrangian multiplier functions is discussed.
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