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]
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())