A descent method for nonsmooth multiobjective optimization problems on Riemannian manifolds
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866929672487436288 |
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| author | Tang, Chunming He, Hao Jian, Jinbao Chao, Miantao |
| author_facet | Tang, Chunming He, Hao Jian, Jinbao Chao, Miantao |
| contents | In this paper, a descent method for nonsmooth multiobjective optimization problems on complete Riemannian manifolds is proposed. The objective functions are only assumed to be locally Lipschitz continuous instead of convexity used in existing methods. A necessary condition for Pareto optimality in Euclidean space is generalized to the Riemannian setting. At every iteration, an acceptable descent direction is obtained by constructing a convex hull of some Riemannian $\varepsilon$-subgradients. And then a Riemannian Armijo-type line search is executed to produce the next iterate. The convergence result is established in the sense that a point satisfying the necessary condition for Pareto optimality can be generated by the algorithm in a finite number of iterations. Finally, some preliminary numerical results are reported, which show that the proposed method is efficient. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_11990 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A descent method for nonsmooth multiobjective optimization problems on Riemannian manifolds Tang, Chunming He, Hao Jian, Jinbao Chao, Miantao Optimization and Control 65K05, 90C30 In this paper, a descent method for nonsmooth multiobjective optimization problems on complete Riemannian manifolds is proposed. The objective functions are only assumed to be locally Lipschitz continuous instead of convexity used in existing methods. A necessary condition for Pareto optimality in Euclidean space is generalized to the Riemannian setting. At every iteration, an acceptable descent direction is obtained by constructing a convex hull of some Riemannian $\varepsilon$-subgradients. And then a Riemannian Armijo-type line search is executed to produce the next iterate. The convergence result is established in the sense that a point satisfying the necessary condition for Pareto optimality can be generated by the algorithm in a finite number of iterations. Finally, some preliminary numerical results are reported, which show that the proposed method is efficient. |
| title | A descent method for nonsmooth multiobjective optimization problems on Riemannian manifolds |
| topic | Optimization and Control 65K05, 90C30 |
| url | https://arxiv.org/abs/2304.11990 |