The title of an old paper..... It mentions that in order to use the full information of a hessian in 2nd order optimization that you should make a part of your iterative step to include v (eigenvector corresponding to smallest eigenvalue, assuming that the eigenvalue is negative).(adsbygoogle = window.adsbygoogle || []).push({});

By doing the following: p = -sign(g'*v)*v : where g is the gradient. So here is the question, what is the geometrical meaning of the dot product of {g,v}? Because the idea is to find a local minimum but I'm trying to find a local maximum and would like to use similar information. Another condition for a local minimum would be that all the eigenvalues are positive, so in my case I would want all of them to be negative. So in my case would I set

p = + or - sign(g'*w)*w, where w is the eigenvalue corresponding to the largest eigenvalue (assuming that its also greater than 0 -- obviously if max(eigenvalue) < 0 then hessian is sufficiently conditioned to find a maximizer. Anyway, I appreciate any help on this.... which sign do I pick and why (what's the geometry behind it?)

Thanks

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Exploiting Directions of Negative Curvature

**Physics Forums | Science Articles, Homework Help, Discussion**