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Constrained minimization

From: Windhorn, Allen E [ACIM/LSA/MKT]
Subject: Constrained minimization
Date: Tue, 31 Dec 2019 19:31:42 +0000

I have a minimization problem involving optimizing the geometry of a curved
surface (pole head shape on a salient-pole generator, if anyone is interested).
There are a number of options available for this including sqp, fminsearch,
fminunc, fmincon, and nonlin_min.  I'm not sure which to use.  Since I have
constraints I have started with sqp, which seems to be the preferred one.

I have some questions about the functionality of sqp, in particular, about the
form of the constraint functions (designated as g and h for equality and
inequality functions).  According to the documentation, these accept the
input vector X and produce an output vector.

1. Does this output vector have to be the same length as the input vector?
If so, what if there are more constraints than components?  Or fewer?
2. Is there supposed to be any correlation between the components of the
output vector and the input vector?  In other words, does output G(1) have
to depend on X(1) in some manner?  Or does the routine make its own
determination of how the output depends on the input?

Also, more generally:

3. What happens if the objective function gets driven into an infeasible
region, such that it produces N/A, NAN, or Inf as an output?  Will the routine
crash?  If so, can I deal with this in a wrapper function?  If so, what output
should be provided -- just a very high number?
4. Is there any documentation of the algorithm sqp uses?
5. Are any of the other options preferable to sqp?

Thanks again for your assistance.

Allen Windhorn P.E. (Mn), CEng| Senior Principal Engineer
Leroy-Somer Americas | Kato Engineering, Inc.
2075 Howard Dr. West | North Mankato, MN 56003 | USA
T +1 507-345-2782 | F +1 507-345-2798
address@hidden | address@hidden

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