# Solvers

{{uranie}} proposes different Nlopt solvers. For direct solvers, there is:

- `TNloptCobyla`: *Constrained Optimization BY Linear Approximation* from M.J.D.Powell works. The 
only direct algorithm that supports constraints naturally.

- `TNloptBobyqa`: *Bounded Optimization BY Quadratic Approximation* from M.J.D.Powell works. It is 
usually quicker than the previous one, but might give nonphysical results if the problem should not 
be assumed to be quadratic.

- `TNloptPraxis`: It uses the *PRincipal AXIS method* of Richard Brend. This algorithm has a 
stochastic part.

- `TNloptNelderMead`: The well known *Nelder-Mead Simplex* algorithm.

- `TNloptSubplexe`: a simplex variant, the Tom Rowan's *subplex* algorithm.

and for gradient-based solvers:

- `TNloptMMA`: *Method of Moving Asymptotes* from Krister Svanberg works. It deals with nonlinear 
inequality constraints naturally.

- `TNloptSLSQP`: *Sequential Least-Squares Quadratic Programming* from Dieter Kraft. It deals with 
both inequality and equality constraints naturally.

- `TNloptLBFGS`: an implementation of the *Limited memory Broyden-Fletcher-Goldfarb-Shanno* 
algorithm written by Ladislaw lukan.
	      
- `TNloptNewtown`: A preconditioned inexact truncated *Newtown* algorithm written by Ladislaw Lukan.

- `TNloptVariableMetric`: An implementation of *shifted limited-memory variable-metric* by Ladislaw 
lukan.

You may notice that actually none of Nlopt global solvers is provided.

```{tip}
Remarks for the gradient case: oftenly one does not have access to the real gradient. In this case a 
finite difference method is used by doing $2n_X+1$ computation around every point, which implies:

- a code that will provide results with a sufficient accuracy so that the gradient is not always 
assumed to be null (which can happen when a code returns a value with a very low number of digits). 
Even with a non-null estimation, the gradient accuracy needs to be sufficient since gradient-based 
solver usually estimates the Hessian matrix.

- a possible parallelisation of the computation.
```