Descent method and line search: quadratic interpolation

[@tarunbhatia8652]

only one video in he entire internet that explains parabolic interpolation so well. Thanks

[@AhmedAli---oc7sk]

You are a life saver .. Thank you.

[@AJ-et3vf]

Great video. Thank you

[@rom_strom]

Fantastic video, thank you

[@flaguser4196]

thanks! looks intuitive and efficient. but wouldn't the gradient still be necessary to define the search line when there are more dimensions?

[@MichelBierlaire]

Not necessarily the gradient. The method can be applied to any descent direction. The point is that the problem of finding a step along a descent direction is a one-dimensional optimization problem, called "linesearch". Quadratic interpolation is just one way to solve it.

[@edikedik8860]

Without taking the derivative, how do we know the location of x*?

[@MichelBierlaire]

x^* is the minimum of a convex parabola.

[@lifecat8452]

Thanks a lot ! I have a question that I hope you can answer. We have obtained the position where ℎ(𝑥∗)achieves its minimum value, that is, when 𝑥=𝑥∗ ,ℎ(𝑥) reaches its minimum. When I set 𝑥∗ = 𝑥𝑘 + 𝛼𝑑𝑘 to find the step size, is it possible for 𝛼 to fall outside the range[0,1]?