An extension of the Karush-Kuhn-Tucker necessity conditions to infinite programming

An extension of the Karush-Kuhn-Tucker necessity conditions to infinite programming

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Article ID: iaor19941934
Country: United States
Volume: 36
Issue: 1
Start Page Number: 1
End Page Number: 17
Publication Date: Mar 1994
Journal: SIAM Math Rev
Authors: ,
Abstract:

Under mild assumptions, the classical Karush-Kuhn-Tucker approach to Lagrange multiplier theory is extended to an infinite programming formulation. The main result generalizes the usual first-order necessity conditions to address problems in which the domain of the objective function is Hilbert space and the number of constraints is arbitrary. The result is used to obtain necessity conditions for a well-known problem from the statistical literature on probability density estimation.

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