دورية أكاديمية
An exact penalty approach for optimization with nonnegative orthogonality constraints
| العنوان: | An exact penalty approach for optimization with nonnegative orthogonality constraints |
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| المؤلفون: | Jiang, Bo, Meng, Xiang, Wen, Zaiwen, Chen, Xiaojun |
| المساهمون: | Massachusetts Institute of Technology. Operations Research Center |
| المصدر: | Springer Berlin Heidelberg |
| بيانات النشر: | Springer Berlin Heidelberg |
| سنة النشر: | 2023 |
| المجموعة: | DSpace@MIT (Massachusetts Institute of Technology) |
| الوصف: | Optimization with nonnegative orthogonality constraints has wide applications in machine learning and data sciences. It is NP-hard due to some combinatorial properties of the constraints. We first propose an equivalent optimization formulation with nonnegative and multiple spherical constraints and an additional single nonlinear constraint. Various constraint qualifications, the first- and second-order optimality conditions of the equivalent formulation are discussed. By establishing a local error bound of the feasible set, we design a class of (smooth) exact penalty models via keeping the nonnegative and multiple spherical constraints. The penalty models are exact if the penalty parameter is sufficiently large but finite. A practical penalty algorithm with postprocessing is then developed to approximately solve a series of subproblems with nonnegative and multiple spherical constraints. We study the asymptotic convergence and establish that any limit point is a weakly stationary point of the original problem and becomes a stationary point under some additional mild conditions. Extensive numerical results on the problem of computing the orthogonal projection onto nonnegative orthogonality constraints, the orthogonal nonnegative matrix factorization problems and the K-indicators model show the effectiveness of our proposed approach. |
| نوع الوثيقة: | article in journal/newspaper |
| وصف الملف: | application/pdf |
| اللغة: | English |
| العلاقة: | https://doi.org/10.1007/s10107-022-01794-8Test; https://hdl.handle.net/1721.1/148140Test; Jiang, Bo, Meng, Xiang, Wen, Zaiwen and Chen, Xiaojun. 2022. "An exact penalty approach for optimization with nonnegative orthogonality constraints." |
| الإتاحة: | https://doi.org/10.1007/s10107-022-01794-8Test https://hdl.handle.net/1721.1/148140Test |
| حقوق: | Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. ; Springer-Verlag GmbH Germany, part of Springer Nature and Mathematical Optimization Society |
| رقم الانضمام: | edsbas.2770BC93 |
| قاعدة البيانات: | BASE |
| الوصف غير متاح. |