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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.29294 |
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| _version_ | 1866911726346174464 |
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| author | Yang, Meijia Xia, Yong |
| author_facet | Yang, Meijia Xia, Yong |
| contents | This paper studies the nonconvex quadratic root-difference minimization under elliptic annulus constraints {\rm (QR)}. We first establish the Annulus Brickman theorem and equivalently reformulate {\rm (QR)} as a 2-dimensional convex problem {\rm (HP)} with hidden variables. We employ the Frank-Wolfe algorithm to globally solve {\rm (HP)}. A key finding is that the solutions of the Frank-Wolfe subproblems, which are traditionally viewed as mere auxiliary updates, are proven to be $O(1/\sqrt{k})$-approximate solutions of the original problem {\rm (QR)}. This transforms an algorithmic by-product into the primary output and completely bypasses the need to solve the computationally expensive quadratic system required for solution recovery. Leveraging this recovery-free property, we develop the efficient Iterative Minimum Generalized Eigenpair (IMGE) algorithm for globally solving {\rm (QR)}. Numerical experiments confirm that IMGE converges rapidly and significantly outperforms conventional methods, especially for large-scale problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_29294 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Global optimization of quadratic root-difference minimization under elliptic annulus constraints Yang, Meijia Xia, Yong Optimization and Control This paper studies the nonconvex quadratic root-difference minimization under elliptic annulus constraints {\rm (QR)}. We first establish the Annulus Brickman theorem and equivalently reformulate {\rm (QR)} as a 2-dimensional convex problem {\rm (HP)} with hidden variables. We employ the Frank-Wolfe algorithm to globally solve {\rm (HP)}. A key finding is that the solutions of the Frank-Wolfe subproblems, which are traditionally viewed as mere auxiliary updates, are proven to be $O(1/\sqrt{k})$-approximate solutions of the original problem {\rm (QR)}. This transforms an algorithmic by-product into the primary output and completely bypasses the need to solve the computationally expensive quadratic system required for solution recovery. Leveraging this recovery-free property, we develop the efficient Iterative Minimum Generalized Eigenpair (IMGE) algorithm for globally solving {\rm (QR)}. Numerical experiments confirm that IMGE converges rapidly and significantly outperforms conventional methods, especially for large-scale problems. |
| title | Global optimization of quadratic root-difference minimization under elliptic annulus constraints |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2605.29294 |