Weak contraction mapping and optimization

Siwei Luo

Abstract: The weak contraction mapping is a self mapping that the range is always a subset of the domain, which admits a unique fixed-point. The iteration of weak contraction mapping is a Cauchy sequence that yields the unique fixed-point. A gradient-free optimization method as an application of weak contraction mapping is proposed to achieve global minimum convergence. The optimization method is robust to local minima and initial point position.

Keywords: Weak contraction mapping, fixed-point theorem, non-convex optimization

TL;DR: A gradient-free method is proposed for non-convex optimization problem