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

*To*: mathgroup at smc.vnet.net*Subject*: [mg55786] Re: [mg55765] Re: NMinimize--problem with a min-max problem*From*: "Janos D. Pinter" <jdpinter at hfx.eastlink.ca>*Date*: Wed, 6 Apr 2005 03:11:19 -0400 (EDT)*References*: <d2tfro$qpe$1@smc.vnet.net> <200504051010.GAA01071@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

David and Jens, in general, one needs to define a closed set for the vars x and y, to guarantee that the model is well-posed. If one sets e.g. x>=0.0001, y>=0.0001, then the warnings disappear. Regards, Janos D. Pinter PCS Inc. E-mail: jdpinter at hfx.eastlink.ca Web: www.pinterconsulting.com At 07:10 AM 4/5/2005, Jens-Peer Kuska wrote: >Hi, > >fun1[z_?NumericQ] := fun1[z] = NMaximize[{( >Log[x] + 4/3 z Log[ >y])/(2 (3/4 + z)), x > 0, y > 0, x + y == 1}, {x, >y}][[1]] > > > >NMinimize[fun1[z], z] > > > >gives several waring messages, because the result >of fun1[] is not always a number, but you get a >result. > >Regards > > Jens > >"David" <isolanoster at gmail.com> schrieb im >Newsbeitrag news:d2tfro$qpe$1 at smc.vnet.net... > > 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 > > > > > > >-- >No virus found in this incoming message. >Checked by AVG Anti-Virus. >Version: 7.0.308 / Virus Database: 266.9.2 - Release Date: 4/5/2005 -- No virus found in this outgoing message. Checked by AVG Anti-Virus. Version: 7.0.308 / Virus Database: 266.9.2 - Release Date: 4/5/2005

**References**:**Re: NMinimize--problem with a min-max problem***From:*"Jens-Peer Kuska" <kuska@informatik.uni-leipzig.de>