OpenMDAO: COBYLA and design variables boundaries

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I am creating this post in the aim to find understand a strange behavior that I noticed when I am trying to use the optimizer COBYLA from the driver ScipyOptimizeDriver. Indeed, when I am trying to solve the Betz limit (which is one the OpenMDAO proposed examples https://openmdao.org/newdocs/versions/latest/examples/betz_limit.html), it sometimes exceeds the boundaries that I set for the design variable "a".

Normally, the variable "a" should always be between 0 and 1. However, by using the same Betz Limit example code and by printing the design variable "a" at each iteration, this is what I get:

 Design iteration number: 1
Input a: [0.5]
Output Cp: [0.5]
 Design iteration number: 2
Input a: [0.5]
Output Cp: [0.5]
 Design iteration number: 3
Input a: [1.5]
Output Cp: [1.5]
 Design iteration number: 4
Input a: [1.]
Output Cp: [0.]
 Design iteration number: 5
Input a: [1.]
Output Cp: [0.]
 Design iteration number: 6
Input a: [1.0625]
Output Cp: [0.01660156]
 Design iteration number: 7
Input a: [1.0078125]
Output Cp: [0.00024605]
 Design iteration number: 8
Input a: [1.00097656]
Output Cp: [3.81842256e-06]
 Design iteration number: 9
Input a: [1.00012207]
Output Cp: [5.96119207e-08]
 Design iteration number: 10
Input a: [1.00001526]
Output Cp: [9.31336785e-10]
 Design iteration number: 11
Input a: [1.00000191]
Output Cp: [1.4551943e-11]
   Normal return from subroutine COBYLA
   NFVALS =   10   F =-0.000000E+00    MAXCV = 0.000000E+00
   X = 1.000000E+00
Optimization Complete
-----------------------------------

Now if you look some iterations: the input a is set to very high value (example: iteration 3 , a=1.5), but the value a should be between 0 and 1 according to the design variable range definition that I set before to launch the optimization. Therefore, I don't understand why I am getting these values when I am selecting COBYLA to solve the Betz Limit problem. Is it part of the COBYLA optimization process, or did I miss something?

Many thanks in advance for your help

openmdao optimization python
1 Answers

COBYLA doesn't natively support (or respect) variable bounds; In the pure Scipy optimizer it will just ignore any bounds you give it. In the OpenMDAO Driver that wraps scipy, we convert the bounds constraints to inequality constraints instead.

In general for any optimizer you can expect inequality constraints to be respected at the converged point (assuming a successful optimization) but they may be violated on the way to that converged point.

I can understand your confusion, since typically bound constraints are treated as hard limits that can NEVER be violated. SLSQP will handle them that way, but COBYLA doesn't. So you get stuck with the weaker inequality constraint formulation instead.

user_23011860
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