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Re: RE: How find the max value of

• To: mathgroup@smc.vnet.net
• Subject: [mg11877] Re: [mg11841] RE: [mg11819] How find the max value of
• From: "Jürgen Tischer" <jtischer@pitagoras.univalle.edu.co>
• Date: Fri, 3 Apr 1998 03:45:34 -0500

I'm afraid Ted, you didn't get the point. The problem isn't about
getting max or min, the problem is about searching for an extreme value
on a non-open set. To tell the truth, apart from doing it the hard way
(first search inside using calculus methods, then search along the
border, then compare what you got) I can't see a way how to do it.

J|rgen


-----Original Message-----
From: Ersek_Ted%PAX1A@mr.nawcad.navy.mil To: mathgroup@smc.vnet.net
<Ersek_Ted%PAX1A@mr.nawcad.navy.mil> Subject: [mg11877] [mg11841] RE: [mg11819]
How find the max value of


>
>barreto"@fec.unicamp.br   wrote:
> ----------
>|
>|w[x_,y_] := Sin[x]*Cos[y];
>|
>|and I need to get the max value of the function in a determinate
>|interval
>|
>|for example
>|
>|
>|{x,0,1},{y,-1,0}
>|How can I do that?
>|
>
>Find the minimum of ( -w[x,y] ) and then change the sign.
>
>You want to find a global minimum.  In order to do that FindMinimum
>needs to  start sufficiently close to the global minimum.  Otherwise it
>will likely  converge on a local minimum that isn't the global minimum.
>You can do that  by sampling the function at the points on a grid, and
>start at the point  where ( -w[x,y] ) is the greatest.  In the lines
>below I hacked out some  code to do this.  If you like you can
>implement this in a package.
>
>In the lines below use it my code on a less trivial example. For this
>example FindMinimum would have worked if it started at almost any
>point in the given interval.  For other examples it will be more
>important  to sample at the points in a grid.
>
>Ted Ersek
>_______________________________
>
>In[1]:=
>w[x_,y_] := Sin[x+Pi/3]*Cos[y+Pi/3]/(x^2+1/2)
>
>In[2]:=
>Module[{pnts, z, biggest, index, start, result}, (
>   pnts=Table[{x,y,w[x,y]},{x,0,2,0.1},{y,-2,0,0.1}];
>   pnts=Flatten[pnts,1];
>   z=Part[Transpose[pnts],3];
>   biggest=Max[z];
>   index=Position[pnts,biggest];
>   index=Part[index,1,1];
>   start=Part[pnts,index];
>   result=FindMinimum[-w[x,y],{x,start[[1]]},{y,start[[2]]}];
>   result/.{dip_,xyvalues_}->{-dip,xyvalues}
> )]
>
>
>Out[2]=
>{1.788104802108598, {x -> 0.1118975014816867,
>   y -> -1.047197650578143}}
>
>