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NLsolve returns a wrong solution without any warning for a slightly modified version of the README example (infeasible by construction):
using NLsolve
function f!(F, x)
F[1]=3*x[1]^2+2*x[1]*x[2]+2*x[2]^2+x[3]+3*x[4]-6
F[2]=2*x[1]^2+x[1]+x[2]^2+3*x[3]+2*x[4]-2
F[3]=3*x[1]^2+x[1]*x[2]+2*x[2]^2+2*x[3]+3*x[4]-1
F[4]=x[1]^2+3*x[2]^2+2*x[3]+3*x[4]-3
end
r = mcpsolve(f!, [0., 0., 0., 0.], [-1, Inf, Inf, Inf],
[1.25, 0., 0., 0.5], reformulation = :smooth, autodiff = :forward)
I would expect NLsolve to return "infeasible" or "not converged". Instead, the output is this:
Results of Nonlinear Solver Algorithm
* Algorithm: Trust-region with dogleg and autoscaling
* Starting Point: [1.25, 0.0, 0.0, 0.5]
* Zero: [0.0, 0.0, 0.0, 1.0]
* Inf-norm of residuals: 0.000000
* Iterations: 3
* Convergence: true
* |x - x'| < 0.0e+00: false
* |f(x)| < 1.0e-08: true
* Function Calls (f): 4
* Jacobian Calls (df/dx): 4
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