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FOAS/Readme.md

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@@ -16,7 +16,7 @@ FOAS is a [first-order nonlinear conjugate method](https://en.wikipedia.org/wiki
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e04kf is also part of the [NAG Optimization Modelling Suite](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04intro.html#optsuite) common handle interface. It offers clarity and consistency of the interface of the solvers within the suite, making it trivial to switch among compatible solvers.
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The following example illustrates the simple usage of FOAS to solve the bound-constrained 2D version of the [Rosenbrock function](https://en.wikipedia.org/wiki/Rosenbrock_function) which is a classical test function to measure and profile performance of solvers. Source of this example is avaible in [Rosenbrock2d.java](example/Rosenbrock2d.java).
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The following example illustrates the simple usage of FOAS to solve the bound-constrained 2D version of the [Rosenbrock function](https://en.wikipedia.org/wiki/Rosenbrock_function) which is a classical test function to measure and profile performance of solvers. Source of this example is avaible in [Rosenbrock2d.java](https://github.com/numericalalgorithmsgroup/NAGJavaExamples/tree/main/FOAS/example/Rosenbrock2d.java). It is also adviced to read this [page](./example) that explains the example.
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<figure style="display:flex;">
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<img src="./images/Rosenbrock2dw.png" width="50%" alt="2D Rosenbrock example"/>
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[Fortran example](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04kff.html#example) |
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[Python example](https://www.nag.co.uk/numeric/py/nagdoc_latest/naginterfaces.library.opt.html#naginterfaces.library.examples.opt.handle_solve_bounds_foas_ex.main) ]
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## A modern replacement for NAG solver [`uncon_conjgrd_comp` (`e04dg`)](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04dgf.html)
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## A modern replacement for NAG solver [uncon_conjgrd_comp (e04dg)](https://www.nag.co.uk/numeric/nl/nagdoc_latest/flhtml/e04/e04dgf.html)
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One of the main design objectives for `handle_solve_bounds_foas` (`e04kf`) was to provide a modern and attractive replacement for the CG solver `e04dg` introduced in Mark 12. While this solver was targeted for unconstrained NLPs, `e04kf` has been extended with an active-set method in order to solve bound-constrained NLPs.
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More recent and modern methods have been incorporated into `e04kf` making it much faster than `e04dg`. The following Figure 2 reports performance profiles over 114 unconstrained NLP CUTEst problems for both solvers `e04kf` and `e04dg`. Contrasting the three plots, it is evident that the new solver is more efficient in time (40% faster) and in general terms is less expensive: requires less function and gradient evaluations.
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[`e04kfc`](https://www.nag.co.uk/numeric/nl/nagdoc_latest/clhtml/e04/e04kfc.html)):
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* [Java](./migration/Migration_E04DG_E04KF.java)
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* [Java](https://github.com/numericalalgorithmsgroup/NAGJavaExamples/tree/main/FOAS/migration/Migration_E04DG_E04KF.java)
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* [Fortran 90](https://www.nag.com/numeric/nl/nagdoc_latest/flhtml/genint/replace.html#e04dgf)
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* [C](https://www.nag.com/numeric/nl/nagdoc_latest/clhtml/genint/replace.html#e04dgc)
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* [Python](https://github.com/numericalalgorithmsgroup/NAGPythonExamples/blob/master/local_optimization/FOAS/migration/migration_e04dg_e04kf.ipynb)

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