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MathGroup Archive 2007

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NMinimize and Constraints

  • To: mathgroup at smc.vnet.net
  • Subject: [mg73759] NMinimize and Constraints
  • From: "janos" <janostothmeister at gmail.com>
  • Date: Tue, 27 Feb 2007 05:55:22 -0500 (EST)

We should like to minimize a matrix function with positivity
constraints and receive negative answer.
Here is our program (sorry, I could not simplify it further):

interpol4[P_] := Module[
{A, a, b, c, d, X, aa, elem, celesfelt},
    A = {{a, b}, {c, d}};
    X := Simplify[Inverse[A].P];
    dis[aa_] := Tr[( aa - IdentityMatrix[2]).Transpose[aa -
IdentityMatrix[2]]];
    elem = Join[{a > 0, b > 0, c > 0, d > 0},
Thread[Flatten[Simplify[X ]] > 0]];
    celesfelt = Join[{dis[A] + dis[X]}, elem];
    {A, X, Thread[Flatten[Simplify[X]] > 0]} /. NMinimize[celesfelt,
{a, b, c,d}]=E3=80=9A2=E3=80=9B
    ]
P = {{1.3125461545700279`, 0.31851196579139557`}, {
        0.0029101631196892354`, 2.047721830824522`}};

interpol4[P]

\!\({{{0.029669424963771507`, 1.106047954322385`}, {1.43581203825442`,
\
0=2E002452321867187179`}}, {{\(-3.571317861253324`*^-9\),
1=2E4257502818374637`}, \
{1.1866991386283172`, 0.24972766660606688`}}, {False, True, True,
True}}\)

Is there any way to enforce NMinimize to take into consideration the
constraint seriously ?

Thanks,

Janos



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