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A complement to the differentiability of saddle points and min‐max
Author(s) -
Delfour M. C.,
Morgan J.
Publication year - 1992
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/oca.4660130107
Subject(s) - infimum and supremum , differentiable function , complement (music) , saddle point , mathematics , saddle , object (grammar) , pure mathematics , function (biology) , mathematical analysis , mathematical optimization , computer science , geometry , biochemistry , chemistry , artificial intelligence , complementation , evolutionary biology , biology , gene , phenotype
The object of this communication is to complement theorems on the differentiability of an infimum, a supremum, a min‐max or a saddle point with respect to a parameter t ≥ 0 at t = 0. This technical result gives an interesting description of the non‐differentiability in some problems with a non‐differentiable cost function subject to a state equation. An example is given along with generalizations of the conclusions of the above theorems.