[Ipopt] Do quasi-Newton methods check the second-order optimality condition?

[Jingxin Ye]

Hi,

When quasi-Newton methods are used, Hessian matrix is approximated. It
seems to be impossible for them to check the second optimality condition.

When Ipopt is set to use quasi-Newton methods, does it check the
second-order optimality condition? If yes, what kind of techniques does it
use to compute the hessian matrix? finite difference?

Thanks,
Jingxin
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