## Expand description

## §cobyla - a pure Rust implementation

COBYLA is an algorithm for minimizing a function of many variables. The method is derivatives-free (only the function values are needed) and take into account constraints on the variables. The algorithm is described in:

M.J.D. Powell, “A direct search optimization method that models the objective and constraint functions by linear interpolation,” in Advances in Optimization and Numerical Analysis Mathematics and Its Applications, vol. 275 (eds. Susana Gomez and Jean-Pierre Hennart), Kluwer Academic Publishers, pp. 51-67 (1994).

The algorithm comes into two flavours :

- As an argmin solver, the Rust code was generated from the C code from here
- As a function
`minimize`

, the Rust code was generated from the C code of the NLopt project (version 2.7.1)

In both cases, an initial transpilation was done with c2rust then the code was manually edited to make it work. The callback mechanismn is inspired from the Rust binding of NLopt, namely rust-nlopt

### §Example

```
cargo run --example paraboloid
```

### §Related projects

- rust-nlopt: the Rust binding of the NLopt project
- argmin: the pure-Rust optimization framework
- slsqp: a pure Rust implementation of the SLSQP algorithm.

### §License

The project is released under MIT License.

## Structs§

- Argmin Solver which implements COBYLA method.
- Maintains the state from iteration to iteration of the crate::CobylaSolver.
- Tolerances used as termination criteria. For all, condition is disabled if value is not strictly positive.

## Enums§

- Failed termination status of the optimization process
- An enum for specifying the initial change of x which correspond to the
`rhobeg`

argument of the original Powell’s algorithm (hence the name) - Successful termination status of the optimization process

## Traits§

- A trait representing objective and constraints functions.

## Functions§

- Minimizes a function using the Constrained Optimization By Linear Approximation (COBYLA) method.