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MathGroup Archive 1998

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Re: RE: How find the max value of



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}}
>
>




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