[Ipopt] optimality of solution

[Hossein Haghighat]

Hello,
I have solved a nonconvex EPEC (equilibrium model
with equilibrium constraints) model with Ipopt, using two modeling
approaches involving:
1- an NLP approach, where the problem is reformulated as a set of nonlinear
equations,
2- a diagonalization approach where the problem is reformulated as a set of
MPECs (mathematical problem with equilibrium constraints)

I get the same solution from these different approaches which supports the
optimality of the solution.
Is there any other way to ensure that the solution is indeed optimal not
a saddle point or a local maximum? (e.g by using IPOPT options,
or initial point manipulations)

thank you in advance,
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