[resend] large input to NMinimize causes NMinimize:"bcons" along with Less:nord ... and I don't think it should

• To: mathgroup at smc.vnet.net
• Subject: [mg72412] [resend] large input to NMinimize causes NMinimize:"bcons" along with Less:nord ... and I don't think it should
• From: "Chris Chiasson" <chris at chiasson.name>
• Date: Wed, 27 Dec 2006 05:06:59 -0500 (EST)
• References: <acbec1a40612222206j4487908drc5d40e8e07900912@mail.gmail.com>

```I am resending this message from the 23rd because it did not appear on
comp.soft-sys.math.mathematica even after the recent batch of reposts:

of course, I've been wrong plenty of times before:

the Piecewise statements in the input (before a replacement for and
application of Simplify) looked like

Piecewise[{{y,Im[y]==0&&y<h[i]/2}},h[i]/2]

so, I believe NMinimize is doing some kind of optimization that
changes evaluation order when it emits Less::nord: Invalid comparison
with 0.+24.351659151792298` I attempted.

In addition, NMinimize:"bcons" says that my constraints aren't
equalities, inequalities, or domain specifications, but I can't see
what is wrong.

It is worth noting that Method->"DifferentialEvolution" will produce
an answer and not complain about the constraints, but it is really the
wrong type of method for this problem (I need one that is derivative
based).

Would someone mind telling me what is producing the Less:nord errors
and why NMinimize can't make up its mind about whether I've given
proper constraints?

here is the input:

NMinimize[{b[1]*h[1] + b[2]*h[2] + b[3]*h[3] + b[4]*h[4] + b[5]*h[5],
-1 + Sqrt[(9000000000000*Piecewise[{{Sqrt[-200/3 + h[1]^2]/2,
Im[Sqrt[-200 + 3*h[1]^2]] == 0 &&
Sqrt[-600 + 9*h[1]^2] < 3*h[1]}}, h[1]/2]^2)/(b[1]^2*h[1]^6) +
(16875000000*(h[1]^2 - 4*Piecewise[{{Sqrt[-200/3 + h[1]^2]/2,
Im[Sqrt[-200 + 3*h[1]^2]] == 0 &&
Sqrt[-600 + 9*h[1]^2] < 3*h[1]}},
h[1]/2]^2)^2)/(b[1]^2*h[1]^6)]/140000000 <= 0 &&
-1 + Sqrt[(5.759999999712*^12*Piecewise[{{Sqrt[-42.66666666453333 +
h[2]^2]/2,
Im[Sqrt[-127.9999999936 + 3*h[2]^2]] == 0 &&
Sqrt[-383.9999999808 + 9*h[2]^2] < 3*h[2]}}, h[2]/2]^2)/
(b[2]^2*h[2]^6) + (16875000000*(h[2]^2 -
4*Piecewise[{{Sqrt[-42.66666666453333 + h[2]^2]/2,
Im[Sqrt[-127.9999999936 + 3*h[2]^2]] == 0 &&
Sqrt[-383.9999999808 + 9*h[2]^2] < 3*h[2]}}, h[2]/2]^2)^
2)/(b[2]^2*h[2]^6)]/140000000 <= 0 &&
-1 + Sqrt[(3.239999999784*^12*Piecewise[{{Sqrt[-23.9999999984 +
h[3]^2]/2, Im[Sqrt[-71.9999999952 + 3*h[3]^2]] ==
0 && Sqrt[-215.9999999856 + 9*h[3]^2] < 3*h[3]}},
h[3]/2]^2)/(b[3]^2*h[3]^6) +
(16875000000*(h[3]^2 - 4*Piecewise[{{Sqrt[-23.9999999984 +
h[3]^2]/2, Im[Sqrt[-71.9999999952 + 3*h[3]^2]] ==
0 && Sqrt[-215.9999999856 + 9*h[3]^2] < 3*h[3]}},
h[3]/2]^2)^2)/(b[3]^2*h[3]^6)]/140000000 <= 0 &&
-1 + Sqrt[(1.439999999856*^12*Piecewise[{{Sqrt[-10.6666666656 +
h[4]^2]/2, Im[Sqrt[-31.9999999968 + 3*h[4]^2]] ==
0 && Sqrt[-95.9999999904 + 9*h[4]^2] < 3*h[4]}},
h[4]/2]^2)/(b[4]^2*h[4]^6) +
(16875000000*(h[4]^2 - 4*Piecewise[{{Sqrt[-10.6666666656 +
h[4]^2]/2, Im[Sqrt[-31.9999999968 + 3*h[4]^2]] ==
0 && Sqrt[-95.9999999904 + 9*h[4]^2] < 3*h[4]}},
h[4]/2]^2)^2)/(b[4]^2*h[4]^6)]/140000000 <= 0 &&
-1 + Sqrt[(3.59999999928*^11*Piecewise[{{Sqrt[-2.666666666133333 +
h[5]^2]/2, Im[Sqrt[-7.9999999984 + 3*h[5]^2]] ==
0 && Sqrt[-23.9999999952 + 9*h[5]^2] < 3*h[5]}},
h[5]/2]^2)/(b[5]^2*h[5]^6) +
(16875000000*(h[5]^2 - 4*Piecewise[{{Sqrt[-2.666666666133333 +
h[5]^2]/2,
Im[Sqrt[-7.9999999984 + 3*h[5]^2]] == 0 &&
Sqrt[-23.9999999952 + 9*h[5]^2] < 3*h[5]}}, h[5]/2]^2)^2)/
(b[5]^2*h[5]^6)]/140000000 <= 0 &&
-1 + (3*Sqrt[3]*Sqrt[(h[5]^2 - 4*Piecewise[{{Sqrt[h[5]^2]/2,
Sqrt[3]*Im[Sqrt[h[5]^2]] == 0 && 3*Sqrt[h[5]^2] <
3*h[5]}}, h[5]/2]^2)^2/(b[5]^2*h[5]^6)])/5600 <= 0
&& -20*b[1] + h[1] <= 0 &&
-20*b[2] + h[2] <= 0 && -20*b[3] + h[3] <= 0 && -20*b[4] + h[4] <=
0 && -20*b[5] + h[5] <= 0 &&
-1 + 0.025/Abs[2.5*^-12*(-5400000/(b[1]*h[1]^3) -
4200000/(b[2]*h[2]^3) - 3000000/(b[3]*h[3]^3) -
1800000/(b[4]*h[4]^3)) +
8.333333333333333*^-13*(-8400000/(b[1]*h[1]^3) +
(12*(-550000 - (1350000*b[2]*h[2]^3)/(b[1]*h[1]^3)))/(b[2]*h[2]^3) +
(12*(-400000 + (b[3]*(-5400000/(b[1]*h[1]^3) -
4200000/(b[2]*h[2]^3))*h[3]^3)/4))/(b[3]*h[3]^3) +
(12*(-250000 + (b[4]*(-5400000/(b[1]*h[1]^3) -
4200000/(b[2]*h[2]^3) - 3000000/(b[3]*h[3]^3))*h[4]^3)/4))/
(b[4]*h[4]^3)) - 1.*^-6/(b[5]*h[5]^3)] <= 0 && 1/100 - b[1]
<= 0 && 1/20 - h[1] <= 0 &&
1/100 - b[2] <= 0 && 1/20 - h[2] <= 0 && 1/100 - b[3] <= 0 && 1/20
- h[3] <= 0 && 1/100 - b[4] <= 0 &&
1/20 - h[4] <= 0 && 1/100 - b[5] <= 0 && 1/20 - h[5] <= 0}, {b[1],
b[2], b[3], b[4], b[5], h[1], h[2], h[3], h[4],
h[5]}]

--
http://chris.chiasson.name/

```

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