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emmt committed Sep 21, 2023
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Expand Up @@ -17,18 +17,18 @@ variables.

Five algorithms are provided:

- `uobyqa` for *Unconstrained Optimization BY Quadratic Approximations* is for
- `uobyqa` (*Unconstrained Optimization BY Quadratic Approximations*) is for
unconstrained optimization, that is `Ω = ℝⁿ`;

- `newuoa` for *Unconstrained Optimization BY Quadratic Approximations* is also
- `newuoa` (*Unconstrained Optimization BY Quadratic Approximations*) is also
for unconstrained optimization (according to M.J.D. Powell, `newuoa` is
superior to `uobyqa`);

- `bobyqa` for *Bounded Optimization BY Quadratic Approximations* is for
simple bound constrained problems;
- `bobyqa` (*Bounded Optimization BY Quadratic Approximations*) is for simple
bound constrained problems;

- `cobyla` for *Constrained Optimization BY Linear Approximations* is for
general constrained problems;
- `cobyla` (*Constrained Optimization BY Linear Approximations*) is for general
constrained problems;

- `lincoa` is also for general constrained problems but, compared to `cobyla`,
linear equality and inequality constraints can be explicitly specified for
Expand All @@ -45,12 +45,11 @@ x, fx, nf, rc, cstrv = cobyla(f, x0; kwds...)
x, fx, nf, rc, cstrv = lincoa(f, x0; kwds...)
```

where `$optim` is one of `uobyqa`, `newuoa`, `bobyqa`, `cobyla`, or `lincoa`,
`f` is the objective function, and `x0` is the initial solution. Constraints
and options may be specified by keywords `kwds...` (see below). The result is
the 4-tuple `(x, fx, nf,rc)` or the 5-tuple `(x, fx, nf, rc, cstrv)` where `x`
is the (approximate) solution found by the algorithm, `fx` is the value of
`f(x)`, `nf` is the number of calls to `f`, `rc` is a status code (an
where `f` is the objective function and `x0` is the initial solution.
Constraints and options may be specified by keywords `kwds...` (see below). The
result is the 4-tuple `(x, fx, nf, rc)` or the 5-tuple `(x, fx, nf, rc, cstrv)`
where `x` is the (approximate) solution found by the algorithm, `fx` is the
value of `f(x)`, `nf` is the number of calls to `f`, `rc` is a status code (an
enumeration value of type `PRIMA.Status`), and `cstrv` is the amount of
constraint violation.

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