A Quadratically Convergent Alternating Projection Method for Nonconvex Sets
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866914173699489792 |
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| author | Xiao, Nachuan Wang, Shiwei Tang, Tianyun Toh, Kim-Chuan |
| author_facet | Xiao, Nachuan Wang, Shiwei Tang, Tianyun Toh, Kim-Chuan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_22916 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Quadratically Convergent Alternating Projection Method for Nonconvex Sets Xiao, Nachuan Wang, Shiwei Tang, Tianyun Toh, Kim-Chuan Optimization and Control 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. |
| title | A Quadratically Convergent Alternating Projection Method for Nonconvex Sets |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2511.22916 |