I had my "aha moment" here when you multiplied the grad by the delta to calculate the directional derivative and then the resulting term resembled the second term of the multi-variate Taylor series. Thank you very much.
Convex problem means it can be approximated locally by a convex quadratic function. The quadratic function being convex is equivalent to the hessian being positive definite.
I had my "aha moment" here when you multiplied the grad by the delta to calculate the directional derivative and then the resulting term resembled the second term of the multi-variate Taylor series. Thank you very much.
Well visualized coherent presentation of a seemingly easy but really difficult topic for intuitive comprehension.
great work...
Thanks for the video! You mention around 5:27 that: 'our hessian will be positive definite whenever our problem is convex'. Why is this the case?
Convex problem means it can be approximated locally by a convex quadratic function. The quadratic function being convex is equivalent to the hessian being positive definite.