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A parametric embedding for the finite minimax problem

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  • Francisco Guerra
  • Guillermo López

Abstract

We consider unconstrained finite minimax problems where the objective function is described as a maximum of functions f k ∈C 3 (ℜ n ,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. Copyright Springer-Verlag Berlin Heidelberg 1999

Suggested Citation

  • Francisco Guerra & Guillermo López, 1999. "A parametric embedding for the finite minimax problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 49(3), pages 359-371, July.
    • Handle: RePEc:spr:mathme:v:49:y:1999:i:3:p:359-371
    DOI: 10.1007/s001860050054
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