Task: Summarization
Input (English): 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.
Output (English): A gradient-free method is proposed for non-convex optimization problem