1

Let's say I have a function $f:\mathbb{R^n} \rightarrow \mathbb{R}, f \in C^2 $ and $x^k \in \mathbb{R^n}$ such that $\nabla f(x^k) = 0 $, but $\nabla ^2f(x^k) $ is not positive semi-definite, can I find a direction $d$ such that a point $x^{k+1} = x^k + \lambda d, \lambda \in [0,1]$ gives me $f(x^{k+1}) < f(x^k)$ ?

Thanks!

Rael
  • 85
  • It seems you are on a saddle point (Or maximum points which will make things even easier). So there is a ball which you are guaranteed to have minimization directions. I'd start checking the Eigen Vectors of the Hessian. I think those which fits negative eigen values will be in directions which minimizes the function. – Royi Sep 24 '17 at 16:48

0 Answers0