Abstract
In this paper, we carry on the analysis (introduced in [4] and developed in [2,7]) of optimality conditions for extremum problems having infinite-dimensional image, in the case of unilateral constraints. This is done by associating to the feasible set a special multifunction. It turns out that the classic Lagrangian multiplier functions can be factorized into a constant term and a variable one; the former is the gradient of a separating hyperplane as introduced in [4,5]; the latter plays the role of selector of the above multifunction. Finally, the need of enlarging the class of Lagrangian multiplier functions is discussed.
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Giannessi, F., Mastroeni, G. & Uderzo, A. On necessary conditions for infinite-dimensional extremum problems. Journal of Global Optimization 28, 319–337 (2004). https://doi.org/10.1023/B:JOGO.0000026452.32070.99
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DOI: https://doi.org/10.1023/B:JOGO.0000026452.32070.99