Question about complex hessian of a barrier function

[alex Sebastian]

Dear ManOpt team, 

I am working on an optimization with a barrier function given by ,

where v is a complex vector at euclidean space, b is a real variable and A is a hermitian matrix.

Now I have difficult to get the hessian about the function at its feasible region. Could you please help me to derive the hessian?

[Nicolas Boumal]

Hello,

Before you get the Hessian, you should get the gradient. What did you obtain for this step, and what steps did you take to check its correctness?

Best,

Nicolas

[alex Sebastian]

Hello,

Thanks for your reply. I have gotten the gradient and passed the gradient check in manopt. Here is the result。

The slope should be 2. It appears to be: 2.00001.

The residual should be 0, or very close. Residual: 3.71409e-16.

Best wishes.