# Analyzing the output of IPOPT

I am solving a feasibility (No objective) problem in IPOPT. I got the following output:

I see that the violation of the constraints are of order 1e-15. What is the meaning of dual infeasibility 1e-07 and the overall NLP error 2e-09? I mean what do they represent if I only have constraints?

$$E_{\mu}(x,\lambda,z) = \max \Big\{ \frac{\| \nabla f(x) + \nabla c(x)\lambda + z \|_\infty}{s_d}, \|c(x)\|_\infty,\frac{\| \text{Diag}(x)\text{Diag(z)}e-\mu e\|_\infty}{s_c} \Big\}$$ Is the the overall NLP error. Dual infeasibility is calculated by $$\| \nabla f(x) + \nabla c(x)\lambda + z \|_\infty$$
The scalings $$s_d$$, $$s_c$$ are explained in the paper on page four. A $$s_d$$ value of around $$50$$ would explain your observation, such a value is allowed to occur. For the meaning of these in the constraint satisfaction case just think $$\nabla f(x) = 0$$.
For a feasibility problem, you can think of the primal objective function as $$f(x) =0$$. These results indicate that your problem was solved—that is, IPOPT found a feasible point.