NMinimize--problem with a min-max problem

*To*: mathgroup at smc.vnet.net*Subject*: [mg55753] NMinimize--problem with a min-max problem*From*: "David" <isolanoster at gmail.com>*Date*: Tue, 5 Apr 2005 03:21:55 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

Hello, I'm trying to solve numerically the following problem: min{z}max{y,x} f{x,y,z} I first do the maximization: fun1[z_] := NMaximize[{( Log[x] + 4/3 z Log[ y])/(2 (3/4 + z)), x > 0, y > 0, x + y == 1}, {x, y}][[1]] I can plot fun1[z] (the solution is at z=.75,x=y=1/2) however NMinimize does accept the definition of fun1[z] as: NMinimize[fun1[z], z] yields error. Any suggestion? Thank you in advance, David