A parametric embedding for the finite minimax problem

A parametric embedding for the finite minimax problem

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Article ID: iaor20002447
Country: Germany
Volume: 49
Issue: 3
Start Page Number: 359
End Page Number: 371
Publication Date: Jan 1999
Journal: Mathematical Methods of Operations Research (Heidelberg)
Authors: ,
Keywords: minimax problem
Abstract:

We consider unconstrained finite minimax problems where the objective function is described as a maximum of functions fk ∈ C3 (ℜn, ℜ). We propose a parametric embedding for the minimax problem and, assuming that the corresponding parametric optimization problem belongs to the generic class of Jongen, Jonker and Twilt, we show that if one applies pathfollowing methods (with jumps) to the embedding in the convex case (in the nonconvex case) one obtains globally convergent algorithms. Furthermore, we prove under usual assumptions on the minimax problem that pathfollowing methods applied to a perturbed parametric embedding of the original minimax problem yield globally convergent algorithms for almost all perturbations.

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