A Proximal Gradient Framework for Composite Multiobjective Optimization on Riemannian Manifolds
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866911690846633984 |
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| author | Chen, Kangming |
| author_facet | Chen, Kangming |
| contents | This paper proposes a Riemannian Multiobjective Proximal Gradient Method (RMPGM) for composite optimization problems on manifolds. Unlike scalarization-based approaches, the proposed framework directly handles vector-valued objectives and establishes global convergence to Pareto stationary points, together with an $\mathcal{O}(1/k)$ convergence rate. We further develop two variants to enhance practicality and performance: an inexact RMPGM that allows controlled inexactness in solving subproblems, and a trust-region RMPGM that adaptively adjusts the penalty parameter and achieves an $\mathcal{O}(ε^{-2}) $iteration complexity. Numerical experiments demonstrate that the proposed methods are consistently outperform subgradient-based baselines. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_16731 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Proximal Gradient Framework for Composite Multiobjective Optimization on Riemannian Manifolds Chen, Kangming Optimization and Control This paper proposes a Riemannian Multiobjective Proximal Gradient Method (RMPGM) for composite optimization problems on manifolds. Unlike scalarization-based approaches, the proposed framework directly handles vector-valued objectives and establishes global convergence to Pareto stationary points, together with an $\mathcal{O}(1/k)$ convergence rate. We further develop two variants to enhance practicality and performance: an inexact RMPGM that allows controlled inexactness in solving subproblems, and a trust-region RMPGM that adaptively adjusts the penalty parameter and achieves an $\mathcal{O}(ε^{-2}) $iteration complexity. Numerical experiments demonstrate that the proposed methods are consistently outperform subgradient-based baselines. |
| title | A Proximal Gradient Framework for Composite Multiobjective Optimization on Riemannian Manifolds |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2605.16731 |