One-sided derivative of min max and saddle points with respect to a parameter ^*

^* The research of the first author has been supported by a Killam Fellowship from Canada Council, Natural Sciences and Engineering Research Council of Canada operating grant A-8730, and a FCAR grant from the “Minitsère de l’éducation du Québec’

Abstract

The object of this paper is to present new theorems on the differentiability of a minimum, maximum, Min Max, or saddle point with respect to a parameter t ⩾ 0 at t = 0 under relaxed assumptions. Those technical results have a wide spectrum of applications: Control Theory, Shape Sensitivity Analysis, Game Theory, etc... In non-differentiable situations they provide an interesting description of the non-differentiability

^* The research of the first author has been supported by a Killam Fellowship from Canada Council, Natural Sciences and Engineering Research Council of Canada operating grant A-8730, and a FCAR grant from the “Minitsère de l’éducation du Québec’

^* The research of the first author has been supported by a Killam Fellowship from Canada Council, Natural Sciences and Engineering Research Council of Canada operating grant A-8730, and a FCAR grant from the “Minitsère de l’éducation du Québec’

Notes

^* The research of the first author has been supported by a Killam Fellowship from Canada Council, Natural Sciences and Engineering Research Council of Canada operating grant A-8730, and a FCAR grant from the “Minitsère de l’éducation du Québec’