I want to find Gradient and hessian of $log(1+x^TAx)$ where $A$ is positive semi definite.

My attempt: $\nabla = x^T(A+A^T)/1+x^TAx$

Hessian = $(A+A^T)(1+x^TAx)-(x^T(A+A^T))^Tx^T(A+A^T)/(1+x^TAx)^2$

Is that correct?

  • $\begingroup$ the last numerator cannot be computed due to a dimension mismatch $\endgroup$ – LinAlg Oct 11 '18 at 21:59
  • $\begingroup$ @LinAlg thanks! Edited, is that correct now? $\endgroup$ – Studying Optimization Oct 11 '18 at 22:04
  • $\begingroup$ seems like it, but if you are unsure you can always check the answer numerically $\endgroup$ – LinAlg Oct 11 '18 at 22:20
  • $\begingroup$ You could use more parentheses. $\endgroup$ – amd Oct 11 '18 at 22:43
  • $\begingroup$ Sounds correct to me..... $\endgroup$ – Mostafa Ayaz Oct 11 '18 at 23:16

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