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MathGroup Archive 2006

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Re: Problem with Minimize function

  • To: mathgroup at smc.vnet.net
  • Subject: [mg71925] Re: Problem with Minimize function
  • From: "Ray Koopman" <koopman at sfu.ca>
  • Date: Mon, 4 Dec 2006 06:38:53 -0500 (EST)
  • References: <ekp4ek$270$1@smc.vnet.net><ekud90$865$1@smc.vnet.net>

amitsoni.1984 at gmail.com wrote:
> I am using following program:
> A = {{2, 4, 5}, {6, 7, 3}, {3, 7, 3}}
> Minimize[-Abs[
>       A[[1, 1]]*q11 + A[[1, 2]]*q21 + A[[1, 3]]*q31 + A[[2, 1]]*q12 +
>         A[[2, 2]]*q22 + A[[2, 3]]*q32 + A[[3, 1]]*q13 + A[[3, 2]]*q23 +
>         A[[3, 3]]*q33],
>   q11^2 + q12^2 + q13^2 == 1 && q11*q21 + q12*q22 + q13*q23 == 0 &&
>     q11*q31 + q12*q32 + q13*q33 == 0 && q21^2 + q22^2 + q23^2 == 1 &&
>     q21*q31 + q22*q32 + q23*q33 == 0 && q31^2 + q32^2 + q33^2 == 1,
> {q11, q12,
>      q13, q21, q22, q23, q31, q32, q33}]
>
> I tried using NMinimize function and it worked fine with it. But I
> could not figure out what is the difference between these two
> functions(Minimize and NMinimize) from their definitions on the
> mathematica website.
>
> Thanks
> Amit

In matrix terms, you're maximizing Tr[A.Q], subject to
Q.Transpose@Q == I. The -Abs wrapper in an unnecessary complication
that makes -Q a solution if Q is a solution.
You want Q = Transpose[First at #.Last@#]&[SingluarValueDecomposition@A]


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