Re: NMinimize--problem with a min-max problem

*To*: mathgroup at smc.vnet.net*Subject*: [mg55804] Re: [mg55753] NMinimize--problem with a min-max problem*From*: Bob Hanlon <hanlonr at cox.net>*Date*: Wed, 6 Apr 2005 03:12:05 -0400 (EDT)*Reply-to*: hanlonr at cox.net*Sender*: owner-wri-mathgroup at wolfram.com

expr=(Log[x]+4/3 z Log[1-x])/(2 (3/4+z)); solnx=Solve[D[expr,x]==0,x][[1]] {x -> 3/(4*z + 3)} solnz=Solve[D[expr/.solnx,z]==0,z][[1]] {z -> 3/4} solnx=solnx/.solnz {x -> 1/2} expr/.solnx/.solnz -((2*Log[2])/3) %//N -0.46209812037329684 Clear[fun1]; fun1[z_?NumericQ] := NMaximize[{(Log[x]+4/3 z Log[1-x])/(2 (3/4+z)), 0<x<1},{x}][[1]]; Off[NMaximize::nnum]; NMinimize[fun1[z],z] {-0.4620981203732968, {z -> 0.7499999786528403}} Bob Hanlon > > From: "David" <isolanoster at gmail.com> To: mathgroup at smc.vnet.net > Date: 2005/04/05 Tue AM 03:21:55 EDT > To: mathgroup at smc.vnet.net > Subject: [mg55804] [mg55753] NMinimize--problem with a min-max problem > > 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 > >