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The initial implementation of this package follows (Dussault, J.-P. 2020):
Adaptive cubic regularization (ARC) and trust-region (TR) methods use modified linear systems to compute their steps. The modified systems consist in adding some multiple of the identity matrix (or a well-chosen positive definite matrix) to the Hessian to obtain a sufficiently positive definite linear system, the so called shifted system. This type of system was first proposed by Levenberg and Marquardt. Some trial and error is often involved to obtain a specified value for this shift parameter. We provide an efficient unified implementation to track the shift parameter; our implementation encompasses many ARC and TR variants.
References
Dussault, J.-P. (2020).
A unified efficient implementation of trust-region type algorithms for unconstrained optimization.
INFOR: Information Systems and Operational Research, 58(2), 290-309.
10.1080/03155986.2019.1624490
Dussault, J.-P., Migot, T. & Orban, D. (2023).
Scalable adaptive cubic regularization methods.
Mathematical Programming.
10.1007/s10107-023-02007-6
How to Cite
If you use AdaptiveRegularization.jl in your work, please cite using the reference given in CITATION.cff.