Hi Arvind,
Unfortunately, there is no way, inside of the multi-start procedure, to make Knitro keep going if it terminates at a stationary point that is not a local solution. If it were a single solve scenario, you could just solve again starting from a small perturbation
of the stationary point solution.
We will consider adding an option for a 2nd order check in a future release (in the case when we have exact 2nd derivatives and the problem is not too large). In our experience, it is rare for Knitro to converge to feasible stationary
points that are not local solutions, but it is possible.
Regards,
-Richard