# A Quadratically Convergent Alternating Projection Method for Nonconvex Sets

arXiv: https://arxiv.org/abs/2511.22916 · HTML: https://mlsanity.com/paper/2511.22916/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Nov 2025.

## Built on by (most cited first, 1 of 1)

- [Optimization over the intersection of manifolds](https://mlsanity.com/paper/2605.22736/) (2026)

## Abstract (arXiv)

In this paper, we consider the feasibility problem, which aims to find a feasible point for the constraint set x ∈ ℝn: c(x) = 0 over a possibly non-regular subset X subset ℝn. Under the constraint nondegeneracy condition, we propose a modified alternating projection method. In our proposed method, based on the concept of projective mapping for X, we alternate a Newton step for finding an inexact solution within the limiting tangent cone of X and a projection to X. Under mild conditions, we prove the local quadratic convergence of our proposed method. Preliminary numerical experiments demonstrate the high efficiency of our proposed alternating projection method.