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MathGroup Archive 2010

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NMINIMIZATION WITH COMPLEX CONJUGATE

  • To: mathgroup at smc.vnet.net
  • Subject: [mg112829] NMINIMIZATION WITH COMPLEX CONJUGATE
  • From: tarun dutta <tarunduttaz at gmail.com>
  • Date: Sat, 2 Oct 2010 05:45:12 -0400 (EDT)

I want to nminimize a function which contain a variable like x[i] and
also its conjugate i.e.x[i]* where       ''i'' can vary from 0 to a
fixed number n the constraint is [sum[abs[x[i]^2=1],
so here I want to find out the value of x[i] for which we will get the
minimized value of the function...

p = 0.05;
q = 1
n = 5;
x[6] = 0;
f = Sum[Sqrt[i + 1] p x[i]
\!\(\*SuperscriptBox[
RowBox[{"(",
RowBox[{"x", "[",
RowBox[{"i", "+", "1"}], "]"}], ")"}], "*"]\) +
\!\(\*SuperscriptBox["p", "*"]\) x[
      i + 1] (x[i])\[Conjugate] + (q*i + i (i - 1)) x[i]
\!\(\*SuperscriptBox[
RowBox[{"(",
RowBox[{"x", "[", "i", "]"}], ")"}], "*"]\), {i, 0, n}];
c = [\!\(
\*UnderoverscriptBox[\(\[Sum]\), \(i = 0\), \(n\)]
\*SuperscriptBox[\(Abs\ [x[i]]\), \(2\)]\) == 1, {i, n}];
v = Array[x, n]; Timing[
 NMinimize[{f, c}, v,
  Method -> {"RandomSearch", Method -> "InteriorPoint"}]]


This is my written program from which I can not get the expected
value.please give a solution...if myproblem is not clear to you people
then just inform me through mailing...


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