Newton-CG methods for nonconvex unconstrained optimization with Hölder continuous Hessian
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866912322847506432 |
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| author | He, Chuan Huang, Heng Lu, Zhaosong |
| author_facet | He, Chuan Huang, Heng Lu, Zhaosong |
| contents | In this paper we consider a nonconvex unconstrained optimization problem minimizing a twice differentiable objective function with Hölder continuous Hessian. Specifically, we first propose a Newton-conjugate gradient (Newton-CG) method for finding an approximate first- and second-order stationary point of this problem, assuming the associated the Hölder parameters are explicitly known. Then we develop a parameter-free Newton-CG method without requiring any prior knowledge of these parameters. To the best of our knowledge, this method is the first parameter-free second-order method achieving the best-known iteration and operation complexity for finding an approximate first- and second-order stationary point of this problem. Finally, we present preliminary numerical results to demonstrate the superior practical performance of our parameter-free Newton-CG method over a well-known regularized Newton method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_13094 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Newton-CG methods for nonconvex unconstrained optimization with Hölder continuous Hessian He, Chuan Huang, Heng Lu, Zhaosong Optimization and Control Machine Learning In this paper we consider a nonconvex unconstrained optimization problem minimizing a twice differentiable objective function with Hölder continuous Hessian. Specifically, we first propose a Newton-conjugate gradient (Newton-CG) method for finding an approximate first- and second-order stationary point of this problem, assuming the associated the Hölder parameters are explicitly known. Then we develop a parameter-free Newton-CG method without requiring any prior knowledge of these parameters. To the best of our knowledge, this method is the first parameter-free second-order method achieving the best-known iteration and operation complexity for finding an approximate first- and second-order stationary point of this problem. Finally, we present preliminary numerical results to demonstrate the superior practical performance of our parameter-free Newton-CG method over a well-known regularized Newton method. |
| title | Newton-CG methods for nonconvex unconstrained optimization with Hölder continuous Hessian |
| topic | Optimization and Control Machine Learning |
| url | https://arxiv.org/abs/2311.13094 |