On minimax optimization problems

We give a short proof that in a convex minimax optimization problem in k dimensions there exist a subset of k + 1 functions such that a solution to the minimax problem with those k + 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.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/47909/1/10107_2005_Article_BF01581038.pd