Hello,
I'm using the Python bindings of NLOPT for derivative based local optimization.
For bound-constrained problems the optimization works fine (using
nlopt.LD_MMA and nlopt.LD_LBFGS).
I now want to solve a problem with a simple linear inequality
constraint `0 >= sum(x) - 10`.
Since I have also some nonlinear equality constraints the only option
seems to be nlopt.LD_AUGLAG (or nlopt.LD_AUGLAG_EQ if I introduce an
additional slack variable).
However, apparently I'm missing something.
1) The problem is differentiable but nlopt failed to find a feasible
solution after hundreds of iterations.
By infeasible I mean that sum(x) is about 100 but it should satisfy
10>= sum(x). I'm pretty confident that the function evaluation and
the gradient/Jacobian evaluation is correct.
2) nlopt.LD_MMA also didn't find a feasible solution
Since it is impossible to post the original problem here I have
adapted the tutorial example and tried to optimize it with
nlopt.LD_AUGLAG.
Code and output below
------------------------------ start test script
-------------------------------------------
import nlopt
from numpy import *
def myfunc(x, grad):
if grad.size > 0:
grad[0] = 0.0
grad[1] = 0.5 / sqrt(x[1])
return sqrt(x[1])
def myconstraint(x, grad, a, b):
if grad.size > 0:
grad[0] = 3 * a * (a*x[0] + b)**2
grad[1] = -1.0
return (a*x[0] + b)**3 - x[1]
def test_LD_MMA():
""" works """
opt = nlopt.opt(nlopt.LD_MMA, 2)
opt.set_lower_bounds([-float('inf'), 0])
opt.set_min_objective(myfunc)
opt.add_inequality_constraint(lambda x,grad: myconstraint(x,grad,2,0), 1e-8)
opt.add_inequality_constraint(lambda x,grad:
myconstraint(x,grad,-1,1), 1e-8)
opt.set_xtol_rel(1e-4)
x = opt.optimize([1.234, 5.678])
minf = opt.last_optimum_value()
print "optimum at ", x[0],x[1]
print "minimum value = ", minf
print "result code = ", opt.last_optimize_result()
def test_LD_AUGLAG():
""" doesn't work """
opt = nlopt.opt(nlopt.LD_AUGLAG, 2)
opt.set_lower_bounds([-float('inf'), 0])
opt.set_maxeval(1000)
opt.set_min_objective(myfunc)
opt.add_inequality_constraint(lambda x,grad: myconstraint(x,grad,2,0), 1e-8)
opt.add_inequality_constraint(lambda x,grad:
myconstraint(x,grad,-1,1), 1e-8)
opt.set_xtol_rel(1e-4)
x = opt.optimize([1.234, 5.678])
minf = opt.last_optimum_value()
print "optimum at ", x[0],x[1]
print "minimum value = ", minf
print "result code = ", opt.last_optimize_result()
def test_LD_AUGLAG_with_set_local_optimizer():
""" doesn't work """
opt = nlopt.opt(nlopt.LD_AUGLAG, 2)
opt.set_local_optimizer(nlopt.LD_MMA)
opt.set_lower_bounds([-float('inf'), 0])
opt.set_min_objective(myfunc)
opt.add_inequality_constraint(lambda x,grad: myconstraint(x,grad,2,0), 1e-8)
opt.add_inequality_constraint(lambda x,grad:
myconstraint(x,grad,-1,1), 1e-8)
opt.set_xtol_rel(1e-4)
x = opt.optimize([1.234, 5.678])
minf = opt.last_optimum_value()
print "optimum at ", x[0],x[1]
print "minimum value = ", minf
print "result code = ", opt.last_optimize_result()
------------------------------ end test script
-------------------------------------------
output of test_LD_MMA():
------------------------------------
optimum at 0.333333331366 0.296296292697
minimum value = 0.544331050646
result code = 4
output of test_LD_AUGLAG():
------------------------------------------
optimum at 0.440450564807 0.0
minimum value = 0.0
result code = 5
output of test_LD_AUGLAG_with_set_local_optimizer():
--------------------------------------------------------------------------------
Traceback (most recent call last):
File "nlopt_test.py", line 70, in <module>
test_LD_AUGLAG_with_set_local_optimizer()
File "nlopt_test.py", line 54, in test_LD_AUGLAG_with_set_local_optimizer
opt.set_local_optimizer(nlopt.LD_MMA)
File
"/home/b45ch1/workspace/tmp/nlopt-2.1.2/lib/python2.6/site-packages/nlopt.py",
line 258, in set_local_optimizer
def set_local_optimizer(*args): return _nlopt.opt_set_local_optimizer(*args)
TypeError: in method 'opt_set_local_optimizer', argument 2 of type
'nlopt::opt const &'
Any input and help would be most welcome.
I'm using NLOPT version:
python -c"import nlopt; print nlopt.version_major(),
nlopt.version_minor(), nlopt.version_bugfix()"
2 2 1
best regards,
Sebastian
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