[Ipopt] Small numbers in constraint

[Thomas Braam]

Hello everyone,

We are doing some modelling of plant metabolism. For this we use Flux
Balance Analysis which represents metabolic networks as a series of linear
differential equations. However, recently we have introduced an additional
equation into the model that describes the exchange of gases (CO2 and water
vapour) between the plant and the atmosphere. This creates a non-linearity
and we have to use a more complex optimisation approach. We are following
the methods described in: https://doi.org/10.1371/journal.pone.0151722 which
uses IPOPT with the HSL-MA97 solver, implemented in Python (PyIpopt).

Our problem is that when we try to implement the scripts with our
gas-exchange equation included, we get a generic numpy error of the type
caused by attempting to divide by 0. The gas-exchange equation (below) does
contain some small numbers, so our first thought is that maybe the error is
caused by IPOPT or PyIpopt rounding down.

Could you confirm if this is something that is not supported by IPOPT (or
something I should generally avoid) or if this is error is possibly
introduced by PyIpopt? Or do you have any ideas for changing the equation
into something I can work with (I am not a mathematician).

Link to equation: https://drive.google.com/file/d/0ByNhotKkxQHMMEZqTk
FrT21xUlBYMElvOVllWGxPcEphb1VV/view?usp=sharing
The variables CwvIn, CwOut, RH & Temp are static (they have equality
bounds), JCO2 has bounds 0 to 1000. The values for the equality bounds that
we use cause the result of the equation to be between 2*JCO2 and 4*JCO2 (if
that makes sense) so the result of the equation is that small.

Many thanks,

Thomas Braam
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