       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
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).Transpose[aa -
IdentityMatrix]];
elem = Join[{a > 0, b > 0, c > 0, d > 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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