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

Author: Zaslavski, Alexander J.

Source: Optimization, Volume 54, Numbers 4-5, -5/August&U8211;October 2005 , pp. 507-516(10)

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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

Document Type: Research article

DOI: http://dx.doi.org/10.1080/02331930500100155

Affiliations: 1: Department of Mathematics, Technion-Israel Institute of Technology, Haifa 32000, Israel

Publication date: 2005-01-01