Gradient Method with Backtracking Parameters alpha and beta

Hello,

I'm having trouble trying to implement the following optimization problem.

There's a lot of function already created that computes the gradient method but I don't know how to implement this problem into them.

https://www.mathworks.com/matlabcentral/fileexchange/35535-simplified-gradient-descent-optimization

Any assistance is greatly apreciated.

Thank You!