Nondifferentiability of an objective function at its point of minimum for most minimax problems

摘要

In this paper we study a class of minimax problems max{f(x), g(x)} → min, x ∈ R~n where f, g ∈ C~l (R~n). We show that the subclass of all problems for which there exists a point of minimum z ∈ R~l such that f(z) = g(z) and ▽f(z) = ▽g(z) is small.