Different Nonlinear Equality and Inequality Constraint Tolerances
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Dear community, I am working on a couple of optimization problems using either the patternsearch or fmincon function and they requrie both nonlinear equality and inequality constraints. The inequality constraints are relatively simple in that they are designed to keep several of the output variables to be between 0 and 1 and the equality constraint are designed so that several output variables equal 1. I would like to apply a different tolerance for the equality and inequality constraints, e.g. 10^-4 for the equality constraints and 10^-6 for the inequality constraints. Is this possible either within the function options or in the constraint function itself?
John D'Errico on 8 Sep 2023
Edited: John D'Errico on 8 Sep 2023
As @Torsten said, the answer is a simple one. No. But sometimes, no can be a fuzzy word. :-)
For example, suppose I have two constraints:
x + y > 1
x*y == 3
By default, these are both constraints, and those tools use ONE constraint tolerance. Suppose you want to have a constraint tolerance of 1e-6 for the inequality, and 1e-4 for the equality constraint? Then multiply the equality constraint by a constant, here scaling it by 0.01.
x + y > 1
x*y/100 == 3/100
Now both sets of constraints can happily live under an overall constraint tolerance of 1e-6.
Simple enough? You cannot change the optimizer. But you CAN change your constraints so you will be happy.
Now, could you send in a feature request to TMW, asking for this capability? Well, yes. But if I were a TB developer, I might respond with exactly this workaround, because adding capability to code where the capability is not needed just makes the code more complex, for no gain.