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@emmt
emmt committed Oct 17, 2023
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Expand Up @@ -49,7 +49,7 @@ package:
equality constraints, and linear inequality constraints.

All these algorithms are trust region methods where the variables are updated
according to an affine or quadratic local approximation interpolating the
according to an affine or a quadratic local approximation interpolating the
objective function at a given number of points (set by keyword `npt` by some of
the algorithms). No derivatives of the objective function are needed. These
algorithms are well suited to problems with a non-analytic objective function
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The keywords allowed by the different algorithms are summarized by the
following table.

| Keyword | Description | Algorithms |
|:-------------|:---------------------------------------|:-----------------------------|
| `rhobeg` | Initial trust region radius | all |
| `rhoend` | Final trust region radius | all |
| `ftarget` | Target objective function value | all |
| `maxfun` | Maximum number of function evaluations | all |
| `iprint` | Verbosity level | all |
| `npt` | Number of points in local model | `bobyqa`, `lincoa`, `newuoa` |
| `xl` | Lower bound | `bobyqa`, `cobyla`, `lincoa` |
| `xu` | Upper bound | `bobyqa`, `cobyla`, `lincoa` |
| `nlconstr` | Non-linear constraints | `cobyla` |
| `eqconstr` | Linear equality constraints | `cobyla`, `lincoa` |
| `ineqconstr` | Linear inequality constraints | `cobyla`, `lincoa` |
| Keyword | Description | Algorithms |
|:-----------------|:---------------------------------------|:-----------------------------|
| `rhobeg` | Initial trust region radius | all |
| `rhoend` | Final trust region radius | all |
| `ftarget` | Target objective function value | all |
| `maxfun` | Maximum number of function evaluations | all |
| `iprint` | Verbosity level | all |
| `npt` | Number of points in local model | `bobyqa`, `lincoa`, `newuoa` |
| `xl` | Lower bound | `bobyqa`, `cobyla`, `lincoa` |
| `xu` | Upper bound | `bobyqa`, `cobyla`, `lincoa` |
| `nonlinear_ineq` | Non-linear inequality constraints | `cobyla` |
| `linear_eq` | Linear equality constraints | `cobyla`, `lincoa` |
| `linear_ineq` | Linear inequality constraints | `cobyla`, `lincoa` |

Assuming `n = length(x)` is the number of variables, then:

Expand Down Expand Up @@ -174,11 +174,11 @@ Assuming `n = length(x)` is the number of variables, then:
elementwise lower and upper bounds for the variables. Feasible variables are
such that `xl ≤ x ≤ xu` (elementwise).

- `nonlinear_ineq` (default `0`) may be specified with the number `m` of
- `nonlinear_ineq` (default `nothing`) may be specified with the number `m` of
non-linear inequality constraints expressed `c(x) ≤ 0`. If the caller is
interested in the values of `c(x)` at the returned solution the keyword may
be set with a vector of `m` double precision floating-point values
to store `c(x)`. This keyword only exists for `cobyla`.
interested in the values of `c(x)` at the returned solution, the keyword may
be set with a vector of `m` double precision floating-point values to store
`c(x)`. This keyword only exists for `cobyla`.

- `linear_eq` (default `nothing`) may be specified as a tuple `(Aₑ,bₑ)` to
represent linear equality constraints. Feasible variables are such that `Aₑ⋅x
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