Multivariate Newton's Method and Optimization - Math Modelling | Lecture 8

In this lecture we introduce Newton's method for root-finding of multivariate functions. This lecture extends our discussion in Lecture 4 for single-variable root-finding. Once the method is introduced, we then apply it to an optimization problem wherein we wish to solve the gradient of a function equal to zero. We demonstrate that Newton's method offers a powerful tool that can complement solving optimization problems.
This course is taught by Jason Bramburger for Concordia University.
More information on the instructor: hybrid.concordia.ca/jbrambur/
Follow @jbramburger7 on Twitter for updates.

[@JosephRivera517]

This is very helpful. I have been looking for a resource to help me with my optimization problem, and this one is gold.

[@derekcobo1453]

Great video. Was very intimidating when I first saw it.

[@nikhilraj4317]

This was very helpful! Thank you!

[@abursuk]

Hey there, thnx for the video! I have a question tho, you mentioned that J matrix should be invertible(means square, means number of variables = number of functions), but I want to find intersection points of 3 (or more) functions(say hyperbolic curves or something similar)? there are only 2 variables: x, y but 3(or more) functions. which means J matrix will not be square -> will not be invertible. Thnx in advance!

[@drioko]

how did this cost you less than a minute running. i programmed this algorithm in my matlab for 10 iterations and it doesn't render the final result its been 10 minutes. do you have a super powerful computer?

[@jasonbramburger]

I suspect you're implementing wrong. Check your Jacobian matrix as this is the main bottleneck.