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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.15632 |
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| _version_ | 1866918063113240576 |
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| author | Hadjisavvas, N. Lara, F. Marcavillaca, R. T. Vuong, P. T. |
| author_facet | Hadjisavvas, N. Lara, F. Marcavillaca, R. T. Vuong, P. T. |
| contents | In this work, we investigate a second-order dynamical system with Hessian-driven damping tailored for a class of nonconvex functions called strongly quasiconvex. Buil\-ding upon this continuous-time model, we derive two discrete-time gra\-dient-based algorithms through time discretizations. The first is a Heavy Ball method with Hessian correction, incorporating cur\-va\-tu\-re-dependent terms that arise from discretizing the Hessian damping component. The second is a Nesterov-type accelerated method with adaptive momentum, fea\-tu\-ring correction terms that account for local curvature. Both algorithms aim to enhance stability and convergence performance, particularly by mi\-ti\-ga\-ting oscillations commonly observed in cla\-ssi\-cal momentum me\-thods. Furthermore, in both cases we establish li\-near convergence to the optimal solution for the iterates and functions values. Our approach highlights the rich interplay between continuous-time dynamics and discrete optimization algorithms in the se\-tting of strongly quasiconvex objectives. Numerical experiments are presented to support obtained results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_15632 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Heavy Ball and Nesterov Accelerations with Hessian-driven Damping for Nonconvex Optimization Hadjisavvas, N. Lara, F. Marcavillaca, R. T. Vuong, P. T. Optimization and Control In this work, we investigate a second-order dynamical system with Hessian-driven damping tailored for a class of nonconvex functions called strongly quasiconvex. Buil\-ding upon this continuous-time model, we derive two discrete-time gra\-dient-based algorithms through time discretizations. The first is a Heavy Ball method with Hessian correction, incorporating cur\-va\-tu\-re-dependent terms that arise from discretizing the Hessian damping component. The second is a Nesterov-type accelerated method with adaptive momentum, fea\-tu\-ring correction terms that account for local curvature. Both algorithms aim to enhance stability and convergence performance, particularly by mi\-ti\-ga\-ting oscillations commonly observed in cla\-ssi\-cal momentum me\-thods. Furthermore, in both cases we establish li\-near convergence to the optimal solution for the iterates and functions values. Our approach highlights the rich interplay between continuous-time dynamics and discrete optimization algorithms in the se\-tting of strongly quasiconvex objectives. Numerical experiments are presented to support obtained results. |
| title | Heavy Ball and Nesterov Accelerations with Hessian-driven Damping for Nonconvex Optimization |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2506.15632 |