A scalable sequential adaptive cubic regularization algorithm for optimization with general equality constraints
Fuente:
arXiv
Guardado en:
| Autores principales: | , , , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866910053191122944 |
|---|---|
| author | Pei, Yonggang Lin, Yubing Shao, Shuai Louzeiro, Mauricio Silva Zhu, Detong |
| author_facet | Pei, Yonggang Lin, Yubing Shao, Shuai Louzeiro, Mauricio Silva Zhu, Detong |
| contents | The scalable adaptive cubic regularization method ($\mathrm{ARC_{q}K}$: Dussault et al. in Math. Program. Ser. A 207(1-2): 191-225, 2024) has been recently proposed for unconstrained optimization. It has excellent convergence properties, well-defined complexity bounds, and promising numerical performance. In this paper, we extend $\mathrm{ARC_{q}K}$ to nonlinear optimization with general equality constraints and propose a scalable sequential adaptive cubic regularization algorithm named $\mathrm{SSARC_{q}K}$. In each iteration, we construct an ARC subproblem with linearized constraints inspired by sequential quadratic optimization methods. Next, a composite-step approach is used to decompose the trial step into the sum of a vertical step and a horizontal step. By means of the reduced-Hessian approach, we rewrite the linearly constrained ARC subproblem as a standard unconstrained ARC subproblem to compute the horizontal step. Analogous to $\mathrm{ARC_{q}K}$, we employ a CG-Lanczos procedure with shifts to solve ARC subproblems inexactly, thus bypassing any hard case consideration. This also avoids solving the subproblem multiple times for obtaining a new iterative point. We establish the global convergence of the inexact ARC method $\mathrm{SSARC_{q}K}$ to first-order critical points. Preliminary numerical tests and some comparison results are presented to illustrate the performance of $\mathrm{SSARC_{q}K}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_11254 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A scalable sequential adaptive cubic regularization algorithm for optimization with general equality constraints Pei, Yonggang Lin, Yubing Shao, Shuai Louzeiro, Mauricio Silva Zhu, Detong Optimization and Control The scalable adaptive cubic regularization method ($\mathrm{ARC_{q}K}$: Dussault et al. in Math. Program. Ser. A 207(1-2): 191-225, 2024) has been recently proposed for unconstrained optimization. It has excellent convergence properties, well-defined complexity bounds, and promising numerical performance. In this paper, we extend $\mathrm{ARC_{q}K}$ to nonlinear optimization with general equality constraints and propose a scalable sequential adaptive cubic regularization algorithm named $\mathrm{SSARC_{q}K}$. In each iteration, we construct an ARC subproblem with linearized constraints inspired by sequential quadratic optimization methods. Next, a composite-step approach is used to decompose the trial step into the sum of a vertical step and a horizontal step. By means of the reduced-Hessian approach, we rewrite the linearly constrained ARC subproblem as a standard unconstrained ARC subproblem to compute the horizontal step. Analogous to $\mathrm{ARC_{q}K}$, we employ a CG-Lanczos procedure with shifts to solve ARC subproblems inexactly, thus bypassing any hard case consideration. This also avoids solving the subproblem multiple times for obtaining a new iterative point. We establish the global convergence of the inexact ARC method $\mathrm{SSARC_{q}K}$ to first-order critical points. Preliminary numerical tests and some comparison results are presented to illustrate the performance of $\mathrm{SSARC_{q}K}$. |
| title | A scalable sequential adaptive cubic regularization algorithm for optimization with general equality constraints |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2503.11254 |