Abstract
Interval methods are used to compute the minimax problem of a twice continuously differentiable functionf(y, z),y ε ℝm,z ε ℝn ofm+n variables over anm+n-dimensional interval. The method provides bounds on both the minimax value of the function and the localizations of the minimax points. Numerical examples, arising in both mathematics and physics, show that the method works well.
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This paper has been written while the first author worked as a visiting professor at the Institut für Angewandte Mathematik of the University of Freiburg i.Br., West Germany. It has been sponsored by Stiftung Volkswagenwerk, number I/63 064. He wishes to thank Professor Dr. K. Nickel for helping him to make his stay possible.
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Zuhe, S., Neumaier, A. & Eiermann, M.C. Solving minimax problems by interval methods. BIT 30, 742–751 (1990). https://doi.org/10.1007/BF01933221
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DOI: https://doi.org/10.1007/BF01933221