# AdaptiveRegularization : A unified efficient implementation of trust-region type algorithms for unconstrained optimization

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.

## 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

## How to Cite

If you use AdaptiveRegularization.jl in your work, please cite using the format given in CITATION.cff. <!–https://citation-file-format.github.io/cff-initializer-javascript/#/ –>

## Installation

pkg> add https://github.com/JuliaSmoothOptimizers/AdaptiveRegularization.jl

## Example

using AdaptiveRegularization, ADNLPModels

# Rosenbrock
nlp = ADNLPModel(x -> 100 * (x[2] - x[1]^2)^2 + (x[1] - 1)^2, [-1.2; 1.0])
stats = ARCqKOp(nlp)

# Bug reports and discussions

If you think you found a bug, feel free to open an issue. Focused suggestions and requests can also be opened as issues. Before opening a pull request, start an issue or a discussion on the topic, please.

If you want to ask a question not suited for a bug report, feel free to start a discussion here. This forum is for general discussion about this repository and the JuliaSmoothOptimizers, so questions about any of our packages are welcome.