AdaptiveRegularization
Documentation for AdaptiveRegularization.
AdaptiveRegularization is a solver for unconstrained nonlinear problems,
min f(x)It uses other JuliaSmoothOptimizers packages for development. In particular, NLPModels.jl is used for defining the problem, and SolverCore.jl for the output.
This package uses Stopping.jl via NLPStopping to handle its workflow, you can also see tutorials with Stopping to learn more.
Algorithm
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.