Abstract
We give a short proof that in a convex minimax optimization problem ink dimensions there exist a subset ofk + 1 functions such that a solution to the minimax problem with thosek + 1 functions is a solution to the minimax problem with all functions. We show that convexity is necessary, and prove a similar theorem for stationary points when the functions are not necessarily convex but the gradient exists for each function.
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Drezner, Z. On minimax optimization problems. Mathematical Programming 22, 227–230 (1982). https://doi.org/10.1007/BF01581038
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DOI: https://doi.org/10.1007/BF01581038