Quadprog - Sometimes non-convex, somtimes convex

I want to maximize the function x'Hx. For that I multiply H by -1 and use quadprog to minimize the resulting problem. I do this for several times using different data. However, Matlab reports that for some runs the problem is non-convex. Now I am wondering how a problem can be convex at one point in time but non-convex at another, as only the input data changes but not the problem itself? Also, in case of a non-convex problem, is Matlab always returning a local minima?

[John D'Errico]

You said that you did it with different data. The thing is, there is NO data used by quadprog, except the matrix H. So if you have changed H on the different runs, the problem has not stayed the same.

[DW]

I have noticed the same behavior, but have been unable to figure out why. Sometimes, multiplying H by -1 results in MATLAB reporting the the problem is non-convex and sometimes it does not and reports a solution. The linear equality constraints are different, but the H is always -1*eye(9).

What is more puzzling is that after updating to MATLAB 2017a (from 2016b), some problems which were previously reported as non-convex now find a solution. The documentation states that the interior-point-convex algorithm must be used if a problem has both linear equality constraints and bounds (which mine does), so I assume that is being used. But that algorithm should only work for a problem with positive definite H. Yet I am able to sometimes get a solution. If anyone has any insight into this behavior, it would be greatly appreciated.

[Moritz Hesse]

This is happening to me as well. A problem which under 2016b was apparently non-convex is suddenly convex after upgrading to 2017b.

As above, any help on this behaviour would be appreciated.