The question is in regards to the step size in using gradient descent to minimize a function. We have a bivariate function: $$F(x_1, x_2) = 0.5(ax_1^2+bx_2^2)$$ For what values of the step size $\gamma$ in gradient descent will the function converge to a local minimum?
I know that if $F$ is convex and $\nabla F$ is Lipschitz continuous, then we can guarantee convergence. My question is for this particular function, can we find a set of values that will guarentee convergence?