A scalable sequential adaptive cubic regularization algorithm for optimization with general equality constraints
Year: 2025
Type: preprint
Abstract: 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 $\mathrm{SSARC_{q}K}$.
Source: arXiv (Cornell University)
Authors: Pei, Yonggang, Lin, Yubing, Shao, Shuai, Louzeiro, Mauricio Silva, Zhu, Detong
Language: English
Subfield: Numerical Analysis
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: 广义非线性分式和问题的全局优化方法研究
OpenAlex ID: W6979341884
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