Strong contraction mapping and topological non-convex optimization

TL;DR

This paper introduces a topological non-convex optimization method based on strong contraction mappings, providing a robust approach to global minimum convergence that is less sensitive to local minima and initial points.

Contribution

It proposes a novel optimization technique leveraging strong contraction mappings to ensure global convergence in non-convex problems.

Findings

Achieves global minimum convergence in non-convex optimization.

Robust to local minima and initial point variations.

Provides theoretical guarantees for fixed-point existence.

Abstract

The strong contraction mapping, a self-mapping that the range is always a subset of the domain, admits a unique fixed-point which can be pinned down by the iteration of the mapping. We introduce a topological non-convex optimization method as an application of strong contraction mapping to achieve global minimum convergence. The strength of the approach is its robustness to local minima and initial point position.