What does fmincon do, specifically, when scaling the tolerance constraint?

That is, what does it mean more specifically when the documentation within the optimization tollbox tolerance details states: 'meaning scale in some sense with problem size or values' . Is it scaling with reference to some initial value? I'm not able to find any more information on this, any help would be appreciated!

Answer 1

[Amit Dhakite]

Hi Peter,

"fmincon()" is a function in the MATLAB Optimization Toolbox used to optimize constrained nonlinear multivariable function.

As the document states, "scale in some sense with problem size or values", it means that the tolerance values can be adjusted automatically based on the characteristics of the optimization problem. The scaling depends on the type of algorithm used by "fmincon()" as well as magnitude of the values of the objective function and the constraints. More information on this can be found in "Tolerances by Solver and Algorithm" in the documentation: https://www.mathworks.com/help/optim/ug/tolerance-details.html

For eg, if the problem involves optimizing a function with very large values, the tolerance constraints might be scaled to a larger absolute value to reflect the magnitude of the function values. Similarly, if the problem has a large number of variables or constraints, the tolerance values might be scaled down to account for the increased complexity of the problem.