# Interior point Newton method

# Optim.IPNewtonType.

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.