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.)"
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