**FISTA**

Fast Iterative Shrinkage-Thresholding Algorithm (FISTA) [Beck09] was one of the first algorithms to use Nesterov’s accelerated gradient descent to speed up the convergence of iterative shrinkage-thresholding (ISTA) from O(β/ε) to O(√(β/ε)). The algorithm and proof sketch for in the previous post based were based on [Bubeck14] and [Beck09] so we’ll skip them. Instead give an R implementation and results that compares ISTA and FISTA performance (in terms of number of iterations) for various step sizes (iterations increase and step size decreases). Continue reading