This model
is obviously infeasible. However SciPy’s SLSQP algorithm returns as if everythin is hunky-dory:
(I hope I did not make a mistake here: things are not as readible as I would like). R also has an interface to SLSQP. Here we see some flags being raised:
> slsqp(c(1,2),
+ function(x) {x[1]^2+x[2]^2},
+ heq=function(x){x[1]+x[2]-1},
+ hin=function(x){x[1]-2},
+ lower=c(0,0))
$par
[1] 1.666667e+00 4.773719e-11
$value
[1] 2.777778
$iter
[1] 105
$convergence
[1] -4
$message
[1] "NLOPT_ROUNDOFF_LIMITED: Roundoff errors led to a breakdown of the optimization algorithm. In this case, the returned minimum may still be useful. (e.g. this error occurs in NEWUOA if one tries to achieve a tolerance too close to machine precision.)"