Nondifferentiability of a cost function at a point of minimum in minimax problems

Abstract

In this article we study a class of minimax problems max {f(x),g(x)}→ min, x ∈ R ¹ where f,g ∈ C ²(R ¹). We show that the subclass of all problems for which there exists a point of minimum z ∈ R ¹ such that f (z) = g(z) and f′(z)=g′(z) is small.

Keywords:

• Complete metric space
• Generic property
• Minimax problem
• Mathematics Subject Classifications 1991: 49J35
• 54E52

Acknowledgments

The author is very grateful to Alexander M. Rubinov for helpful discussions, and to the referee for useful comments.

Notes

Dedicated to V.F. Demyanov on the occasion of his 65th birthday.

Additional information

Notes on contributors

Alexander J. Zaslavski

Dedicated to V.F. Demyanov on the occasion of his 65th birthday.