I'm trying to use the gradient ascent method on a convex function like the multivariate-Normal density function with respect to its parameters (the original is a bit more complicated), something similar to maximum likelihood estimation.
$$a_{n+1}=a_n+\gamma_n\nabla F(a_n)$$
I'm wondering if for the gradient ascent method will misbehave if I use a constant value for the step size, i.e. $\gamma_n=\gamma$.
Also, if I wanted to use an adaptive step size, what would be the simplest, and fastest computationally-wise way to define it?