Simple Academic Use Case with unexpected MMA behavior.

[SimoneConiglio]

Hello,
Doing some tests on multiple starting guess and multiple optimization algorithm I found a case on which your solver behaves unexpectedly.
This is luckily a simple analytical example easily reproducible.

import nlopt
from numpy import array

def f(x, grad):
if grad.size > 0:
grad[0] = 2. * (x[0] - 1.)
grad[1] = 2. * (x[1] - 1.)
return (x[0] - 1.) ** 2. + (x[1] - 1.) ** 2.

def g(x, grad):
if grad.size > 0:
grad[0] = 1.
grad[1] = 1.
return x[0] + x[1] - 1.

if name == "main":
algorithm = nlopt.LD_MMA
n = 2
opt = nlopt.opt(algorithm, n)
lb = array([0., 0.])
ub = array([1., 1.])
x0 = array([0.25, 1])
opt.set_min_objective(f)
opt.set_lower_bounds(lb)
opt.set_upper_bounds(ub)
opt.add_inequality_constraint(g, 1e-3)
tol = 1e-6
maxeval = 50
opt.set_ftol_rel(tol)
opt.set_ftol_abs(tol)
opt.set_xtol_rel(tol)
opt.set_xtol_rel(tol)
opt.set_maxeval(maxeval)
opt.set_param("verbosity", 10000)
opt.set_param("inner_maxeval",10)
xopt = opt.optimize(x0)
print(xopt)
opt_val = opt.last_optimum_value()
print(opt_val)
result = opt.last_optimize_result()
print(result)

The solution to this problem is simply [0.5, 0.5] correctly spotted by LD_MMA from most initial guess but not with the starting guess [0.25,1].

In this case the log looks like that:

MMA dual converged in 6 iterations to g=0.914369:
MMA y[0]=1e+40, gc[0]=0.116025
MMA outer iteration: rho -> 0.1
MMA rhoc[0] -> 0.1
MMA dual converged in 3 iterations to g=1.34431:
MMA y[0]=1e+40, gc[0]=-0.269712
MMA outer iteration: rho -> 0.01
MMA rhoc[0] -> 0.01
MMA sigma[0] -> 0.6
MMA sigma[1] -> 0.6
MMA dual converged in 3 iterations to g=2.23837:
MMA y[0]=1e+40, gc[0]=-0.378669
MMA outer iteration: rho -> 0.001
MMA rhoc[0] -> 0.001
MMA sigma[0] -> 0.6
MMA sigma[1] -> 0.72
MMA dual converged in 3 iterations to g=2.79213:
MMA y[0]=1e+40, gc[0]=-0.454075
MMA outer iteration: rho -> 0.0001
MMA rhoc[0] -> 0.0001
MMA sigma[0] -> 0.6
MMA sigma[1] -> 0.864
MMA dual converged in 3 iterations to g=3.13745:
MMA y[0]=1e+40, gc[0]=-0.524222
MMA outer iteration: rho -> 1e-05
MMA rhoc[0] -> 1e-05
MMA sigma[0] -> 0.6
MMA sigma[1] -> 1.0368
MMA dual converged in 3 iterations to g=2.46249:
MMA y[0]=1e+40, gc[0]=-0.587037
MMA outer iteration: rho -> 1e-05
MMA rhoc[0] -> 1e-05
MMA sigma[0] -> 0.6
MMA sigma[1] -> 1.24416
MMA dual converged in 3 iterations to g=1.81718:
MMA y[0]=1e+40, gc[0]=-0.625775
MMA inner iteration: rho -> 0.0001
MMA rhoc[0] -> 1e-05
MMA dual converged in 3 iterations to g=1.81722:
MMA y[0]=1e+40, gc[0]=-0.625775
MMA inner iteration: rho -> 0.001
MMA rhoc[0] -> 1e-05
MMA dual converged in 3 iterations to g=1.81766:
MMA y[0]=1e+40, gc[0]=-0.625775
MMA inner iteration: rho -> 0.01
MMA rhoc[0] -> 1e-05
MMA dual converged in 3 iterations to g=1.82206:
MMA y[0]=1e+40, gc[0]=-0.625775
MMA inner iteration: rho -> 0.1
MMA rhoc[0] -> 1e-05
MMA dual converged in 3 iterations to g=1.86611:
MMA y[0]=1e+40, gc[0]=-0.625775
MMA inner iteration: rho -> 0.410949
MMA rhoc[0] -> 1e-05
MMA dual converged in 3 iterations to g=2.01828:
MMA y[0]=1e+40, gc[0]=-0.625775
[0.1160254 0.8660254]
0.7993602791855875
3

Your solver stops to the design point [0.1160254 0.8660254] that is nor a local minimum, nor a saddle point for the objective neither a kkt point .
I would like to have your insight on this behavior.
BRs
Simone Coniglio