{"ID":2835361,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.22916","arxiv_id":"2511.22916","title":"A Quadratically Convergent Alternating Projection Method for Nonconvex Sets","abstract":"In this paper, we consider the feasibility problem, which aims to find a feasible point for the constraint set $\\{x \\in \\mathbb{R}^n: c(x) = 0\\}$ over a possibly non-regular subset $\\mathcal{X} \\subset \\mathbb{R}^n$. Under the constraint nondegeneracy condition, we propose a modified alternating projection method. In our proposed method, based on the concept of projective mapping for $\\mathcal{X}$, we alternate a Newton step for finding an inexact solution within the limiting tangent cone of $\\mathcal{X}$ and a projection to $\\mathcal{X}$. 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.","short_abstract":"In this paper, we consider the feasibility problem, which aims to find a feasible point for the constraint set $\\{x \\in \\mathbb{R}^n: c(x) = 0\\}$ over a possibly non-regular subset $\\mathcal{X} \\subset \\mathbb{R}^n$. Under the constraint nondegeneracy condition, we propose a modified alternating projection method. In o...","url_abs":"https://arxiv.org/abs/2511.22916","url_pdf":"https://arxiv.org/pdf/2511.22916v1","authors":"[\"Nachuan Xiao\",\"Shiwei Wang\",\"Tianyun Tang\",\"Kim-Chuan Toh\"]","published":"2025-11-28T06:39:59Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}