# Interior point Newton method

#
** Optim.IPNewton** —

*Type*.

**Interior-point Newton**

**Constructor**

```
IPNewton(; linesearch::Function = Optim.backtrack_constrained_grad,
μ0::Union{Symbol,Number} = :auto,
show_linesearch::Bool = false)
```

The initial barrier penalty coefficient `μ0`

can be chosen as a number, or set to `:auto`

to let the algorithm decide its value, see `initialize_μ_λ!`

.

*Note*: For constrained optimization problems, we recommend always enabling `allow_f_increases`

and `successive_f_tol`

in the options passed to `optimize`

. The default is set to `Optim.Options(allow_f_increases = true, successive_f_tol = 2)`

.

As of February 2018, the line search algorithm is specialised for constrained interior-point methods. In future we hope to support more algorithms from `LineSearches.jl`

.

**Description**

The `IPNewton`

method implements an interior-point primal-dual Newton algorithm for solving nonlinear, constrained optimization problems. See Nocedal and Wright (Ch. 19, 2006) for a discussion of interior-point methods for constrained optimization.

**References**

The algorithm was originally written by Tim Holy (@timholy, tim.holy@gmail.com).

- J Nocedal, SJ Wright (2006), Numerical optimization, second edition. Springer.
- A Wächter, LT Biegler (2006), On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming. Mathematical Programming 106 (1), 25-57.