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MathGroup Archive 2000

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Re: minimizing f(x,y) ???!!!!

  • To: mathgroup at smc.vnet.net
  • Subject: [mg25455] Re: [mg25431] minimizing f(x,y) ???!!!!
  • From: BobHanlon at aol.com
  • Date: Sun, 1 Oct 2000 02:44:39 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

In a message dated 9/29/2000 1:33:03 AM, twirt at hotmail.com writes:

>I never used Mathematica before and want to find the minimum for the
>following function:
>
>  h(a,b) := g(a,b) / f(a,b)
>
>  a [0 .. pi]
>  b [pi-a .. pi]
>
>  f(a,b) := 1/3*(1+1/(4*pi)*(a+b-2*acos(-1-cos(a)- cos(b))))
>  g(a,b) := 1/8*(2-cos(a)-cos(b))
>
>Could anyone give me step by step intructions?
>

f[a_, b_] := 1/3*(1 + 1/(4*Pi)*(a + b - 2*a*Cos[-1 - Cos[a] - Cos[b]]))

g[a_, b_] := 1/8*(2 - Cos[a] - Cos[b])

h[a_, b_] := Evaluate[Simplify[g[a, b] / f[a, b]]]

Plot3D[h[a, b], {a, -2, 2}, {b, -2, 2}];

FindMinimum[h[a, b], {a, 0.1}, {b, 0.1}]

{0., {a -> 7.354659682383383*^-10, 
   b -> -7.126406092436465*^-10}}


Bob Hanlon


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