IF: Iterative Fractional Optimization

Abstract

Most optimization problems lack closed-form solutions of the argument that minimizes a given function, and even if these were available it might be prohibitive to compute it. As such, we rely on iterative numerical algorithms to find an approximate solution. In this paper, we propose to leverage fractional calculus in the context of time series analysis methods to devise a new iterative algorithm. Specifically, we propose to leverage autoregressive fractional-order integrative moving average time series, whose coefficients encode a proxy for local spatial information. We provide evidence that our algorithm is efficient and particularly suitable for cases where the Hessian is ill-conditioned.