# Line Search optimization: Is there a way without gradient?

I was wondering as I was listening to the 'introduction of numerics' lecture whether there is a line search optimization method (e.g. optimizing the step size for a given direction vector) such as Armijo but without needing the gradient of a function?

The problem I am talking about is optimizing $$\alpha$$ in:

$$f(x + \alpha d) < f(x)$$

• Googl4e derivative-free line search May 3, 2020 at 1:35