This feature is long overdue, see also #31. What I would like to do as a first step towards this is to build a simple support function that when given a model and constraints, outputs the Lagrange function to be optimized. Example:
from symfit import parameters, Eq
from symfit.core.support import lagrange_function
x, y = parameters('x, y')
f = x + y
unit_circle = Eq(x**2 + y**2, 1)
model = lagrange_function(f, constraints=[unit_circle])
print(model)
>>> x + y + l1 * (x**2 + y**2 - 1)
This is a very minimal example, in case you don't manually provide parameters to be used as Lagrange multipliers. When you do, feed the constraints argument with a dict instead:
from symfit import parameters, Eq
from symfit.core.support import lagrange_function
l, = parameters('l')
model = lagrange_function(f, constraints={l: unit_circle})
print(model)
>>> x + y + l * (x**2 + y**2 - 1)
This is recommended, since the automatic generation might result in conflicts.
I'm not sure yet if this function should return a Model object, or simply an expression that you yourself can then feed to a model. Probably the latter, since that way you can name the dependent variable yourself.
This model can then be fed to any existing minimizer and it will perform a constraint minimization instead.
Additionally, we can use this same syntax to help Fit distinguish between these approaches as well. If you feed Fit the constraints as a list, it will continue to use SLSQP. If you feed it a dict with parameters as keys instead, it will call this function first and minimize the Lagrange function using whichever minimizer it deems best based on the usual criterions.
fit = Fit(f, constraints={l: unit_circle})
fit_result = fit.execute()
This feature can also be extended to include Karush–Kuhn–Tucker inequality constraints.
This feature is long overdue, see also #31. What I would like to do as a first step towards this is to build a simple support function that when given a model and constraints, outputs the Lagrange function to be optimized. Example:
This is a very minimal example, in case you don't manually provide parameters to be used as Lagrange multipliers. When you do, feed the
constraintsargument with adictinstead:This is recommended, since the automatic generation might result in conflicts.
I'm not sure yet if this function should return a Model object, or simply an expression that you yourself can then feed to a model. Probably the latter, since that way you can name the dependent variable yourself.
This model can then be fed to any existing minimizer and it will perform a constraint minimization instead.
Additionally, we can use this same syntax to help
Fitdistinguish between these approaches as well. If you feedFitthe constraints as a list, it will continue to use SLSQP. If you feed it a dict with parameters as keys instead, it will call this function first and minimize the Lagrange function using whichever minimizer it deems best based on the usual criterions.This feature can also be extended to include Karush–Kuhn–Tucker inequality constraints.