I have a non-convex function as follow
where: $\alpha < 1$ and $\theta \in \bigtriangleup_{K}$ means:
$\theta_1 + \theta_2 + ... + \theta_K = 1$ and $\theta_i \ge \epsilon > 0, \quad i=1,...,K$ ($\epsilon$ is a small constant)
I design a FW algorithm as follows:
How can I evaluate the convergence rate of the algorithm above? Can I change step size to achieve the convergence rate is O(1/t)? (t is number of iterations)