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