Scaling in optimization routines

What optimization routines have built-in problem scaling? I see that fmincon has an option "ScaleProblem." Is the default for this set to true or false? What values are actually scaled? Do other routines have a similar option (for example fminsearch, genetic algorithm, particle swarm, etc.)

Edited to add: There's a change to the values for ScaleProblem as of R2016a. Here's a table of legacy and current values in case you find them helpful.

Answer 1

[Run Zhu]

Hi,

ScaleProblem works in two different ways:

For fmincon using SQP and SQP Legacy algorithms, ScaleProblem will normalize all constraints and the objective function by their initial values when set to 'obj-and-constr'. The default value is 'none'

For fsolve, lsqcurvefit, and lsqnonlin using levenberg-marquardt algorithms, setting the ScaleProblem option to 'jacobian' sometimes helps the solver on badly-scaled problems. The default value is 'none'.

More information can be found in https://www.mathworks.com/help/optim/ug/optimization-options-reference.html