I am trying to supply constraints to a a function minimisation that I have hitherto been performing successfully with an unconstrained algorithm available via scipy (scipy.optimize.fmin_l_bfgs_b()).
Reading up (see, e.g, Python constrained non-linear optimization), I discovered a minimisation packed called mystic that seems to be what I need. My situation is as follows. I have a function of 3N variables (representing xyz position coordinates of N nodes), and I want to supply a list of constraints such that z/x = const. for each node. This makes for a total of N constraints. How do I do define/supply these constraints most efficiently for mystic()? Can the same constraint object be used with scipy.optimize.slsqp() as well? Since my constraints are linear, this should be a viable option too.
I tried the following, but it crashed my computer:
import mystic.symbolic as ms
ieqns = ''
for p in range(N):
ieqns += 'x'+str(p+2) +'/x'+str(p) +" <= 2"
cf = ms.generate_constraint(ms.generate_solvers(ms.simplify(ieqns)))
pf = ms.generate_penalty(ms.generate_conditions(ieqns), k=1e12)
I'm the mystic author. I believe what you are looking to do is something like this:
>>> import mystic.symbolic as ms
>>> ieqns = ''
>>> for p in range(10):
... ieqns += 'x{0} <= 2*x{1}\n'.format(p+2,p)
...
>>> cf = ms.generate_constraint(ms.generate_solvers(ieqns))
>>>
>>> # test that it applies the constraints
>>> cf([1.,3.,5.,7.,9.,11.,13.,15.,17.,19.,21.,23.,25.])
[1.0, 3.0, 2.0, 6.0, 4.0, 11.0, 8.0, 15.0, 16.0, 19.0, 21.0, 23.0, 25.0]
Then we can minimize while applying the constraints (however, in the following case the constraints are basically irrelevant):
>>> # get an objective
>>> import mystic.models as mm
>>> rosen = mm.dejong.Rosenbrock(12).function
>>>
>>> # get an optimizer
>>> import mystic.solvers as my
>>> result = my.diffev2(rosen, x0=bounds, bounds=bounds, constrints=cf, npop=40, disp=False, full_output=True, gtol=100)
>>>
>>> # get the solution
>>> result[0]
array([0.99997179, 1.00005506, 1.00012367, 0.99998539, 0.99984306,
0.99981495, 0.999951 , 0.99996505, 0.99971107, 0.99925239,
0.99846259, 0.99692293])
>>> # and the final 'cost'
>>> result[1]
2.2385442425350018e-05
>>>