Coordinate projected gradient descent minimization and its application to orthogonal nonnegative matrix factorization
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912303744548864 |
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| author | Chorobura, Flavia Lupu, Daniela Necoara, Ion |
| author_facet | Chorobura, Flavia Lupu, Daniela Necoara, Ion |
| contents | In this paper we consider large-scale composite nonconvex optimization problems having the objective function formed as a sum of three terms, first has block coordinate-wise Lipschitz continuous gradient, second is twice differentiable but nonseparable and third is the indicator function of some separable closed convex set. Under these general settings we derive and analyze a new cyclic coordinate descent method, which uses the partial gradient of the differentiable part of the objective, yielding a coordinate gradient descent scheme with a novel adaptive stepsize rule. We prove that this stepsize rule makes the coordinate gradient scheme a descent method, provided that additional assumptions hold for the second term in the objective function. We also present a worst-case complexity analysis for this new method in the nonconvex settings. Numerical results on orthogonal nonnegative matrix factorization problem also confirm the efficiency of our algorithm. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_00770 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Coordinate projected gradient descent minimization and its application to orthogonal nonnegative matrix factorization Chorobura, Flavia Lupu, Daniela Necoara, Ion Optimization and Control In this paper we consider large-scale composite nonconvex optimization problems having the objective function formed as a sum of three terms, first has block coordinate-wise Lipschitz continuous gradient, second is twice differentiable but nonseparable and third is the indicator function of some separable closed convex set. Under these general settings we derive and analyze a new cyclic coordinate descent method, which uses the partial gradient of the differentiable part of the objective, yielding a coordinate gradient descent scheme with a novel adaptive stepsize rule. We prove that this stepsize rule makes the coordinate gradient scheme a descent method, provided that additional assumptions hold for the second term in the objective function. We also present a worst-case complexity analysis for this new method in the nonconvex settings. Numerical results on orthogonal nonnegative matrix factorization problem also confirm the efficiency of our algorithm. |
| title | Coordinate projected gradient descent minimization and its application to orthogonal nonnegative matrix factorization |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2504.00770 |