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Question: How do I solve a variational problem with maple?

Question:How do I solve a variational problem with maple?

kainmuth 5 Maple
optimization calculus-of-variations constraint
March 02 2018
1

Hello!

I am trying to find a minimizer for the functional E (see Maple code), where u is in L2([0,rmax]) (Constraint) and u is approximated by a finite set of fourier coefficients in the basis {n*exp(ikx)}.

I don't have much expirience with maple so I could use some help solving this.

The codes I tried either show an erroer( unexpected parameters) or run a very long time until I interupt.

Do I have something wrong or can I reformulate the problem?

Thank you!

Kainmuth

 

Minimizetest2.mw
 

> 

restart
> 

``
> 

with(Optimization);

[ImportMPS, Interactive, LPSolve, LSSolve, Maximize, Minimize, NLPSolve, QPSolve]

 (1)
> 

rmax := 20;

20

 (2)
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n := 1/sqrt(rmax);

(1/10)*5^(1/2)

 (3)
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const := abs(c1)^2+abs(c2)^2+abs(c3)^2 = 1;

abs(c1)^2+abs(c2)^2+abs(c3)^2 = 1

 (4)
> 

f := proc (x) options operator, arrow; n*c1+n*c2*exp(I*x)+n*c3*exp((2*I)*x) end proc;

proc (x) options operator, arrow; n*c1+n*c2*exp(I*x)+n*c3*exp((2*I)*x) end proc

 (5)
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E := proc (c1, c2, c3) options operator, arrow; int(abs(diff(f(x), x))^2, x = 0 .. rmax)+.5*(int(abs(f(x))^2*w(x-y)*abs(f(y))^2, x = 0 .. rmax)) end proc;

proc (c1, c2, c3) options operator, arrow; int(abs(diff(f(x), x))^2, x = 0 .. rmax)+.5*(int(abs(f(x))^2*w(x-y)*abs(f(y))^2, x = 0 .. rmax)) end proc

 (6)
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Optimization:-Minimize(E(f(x)), const);

Warning,  computation interrupted

  
> 

``


 

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