Global convergence of a modified BFGS-type method based on function information for nonconvex multiobjective optimization problems
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910645073477632 |
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| author | Yang, Yingxue |
| author_facet | Yang, Yingxue |
| contents | In this paper, based on function information, we propose a modified BFGS-type method for nonconvex multiobjective optimization problems (MFQNMO). In the multiobjective quasi-Newton method (QNMO), each iteration involves separately approximating the Hessian matrix for each component objective function, which results in significant storage and computational burdens. MFQNMO employs a common BFGS-type matrix to approximate the Hessian matrix of all objective functions in each iteration. This matrix is updated using function information from the previous step. This approach strikes a balance between efficacy and computational cost. We confirm the convergence of the method without relying on convexity assumptions, under mild conditions, we establish a local superlinear convergence rate for MFQNMO. Furthermore, we validate its effectiveness through experiments on both nonconvex and convex test problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_00543 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Global convergence of a modified BFGS-type method based on function information for nonconvex multiobjective optimization problems Yang, Yingxue Optimization and Control In this paper, based on function information, we propose a modified BFGS-type method for nonconvex multiobjective optimization problems (MFQNMO). In the multiobjective quasi-Newton method (QNMO), each iteration involves separately approximating the Hessian matrix for each component objective function, which results in significant storage and computational burdens. MFQNMO employs a common BFGS-type matrix to approximate the Hessian matrix of all objective functions in each iteration. This matrix is updated using function information from the previous step. This approach strikes a balance between efficacy and computational cost. We confirm the convergence of the method without relying on convexity assumptions, under mild conditions, we establish a local superlinear convergence rate for MFQNMO. Furthermore, we validate its effectiveness through experiments on both nonconvex and convex test problems. |
| title | Global convergence of a modified BFGS-type method based on function information for nonconvex multiobjective optimization problems |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2408.00543 |