Optim.jl
Univariate and multivariate optimization in Julia.
Optim.jl is part of the JuliaNLSolvers family.
For direct contact to the maintainer, you can reach out directly to pkofod on slack.
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Optimization
Optim.jl is a package for univariate and multivariate optimization of functions. A typical example of the usage of Optim.jl is
using Optim
rosenbrock(x) = (1.0 - x[1])^2 + 100.0 * (x[2] - x[1]^2)^2
result = optimize(rosenbrock, zeros(2), BFGS())This minimizes the Rosenbrock function
with a = 1, b = 100 and the initial values x=0, y=0. The minimum is at (a,a^2).
The above code gives the output
* Status: success
* Candidate solution
Minimizer: [1.00e+00, 1.00e+00]
Minimum: 5.471433e-17
* Found with
Algorithm: BFGS
Initial Point: [0.00e+00, 0.00e+00]
* Convergence measures
|x - x'| = 3.47e-07 β° 0.0e+00
|x - x'|/|x'| = 3.47e-07 β° 0.0e+00
|f(x) - f(x')| = 6.59e-14 β° 0.0e+00
|f(x) - f(x')|/|f(x')| = 1.20e+03 β° 0.0e+00
|g(x)| = 2.33e-09 β€ 1.0e-08
* Work counters
Seconds run: 0 (vs limit Inf)
Iterations: 16
f(x) calls: 53
βf(x) calls: 53
To get information on the keywords used to construct method instances, use the Julia REPL help prompt (?)
help?> LBFGS
search: LBFGS
LBFGS
β‘β‘β‘β‘β‘β‘β‘
Constructor
=============
LBFGS(; m::Integer = 10,
alphaguess = LineSearches.InitialStatic(),
linesearch = LineSearches.HagerZhang(),
P=nothing,
precondprep = (P, x) -> nothing,
manifold = Flat(),
scaleinvH0::Bool = true && (typeof(P) <: Nothing))
LBFGS has two special keywords; the memory length m, and
the scaleinvH0 flag. The memory length determines how many
previous Hessian approximations to store. When scaleinvH0
== true, then the initial guess in the two-loop recursion
to approximate the inverse Hessian is the scaled identity,
as can be found in Nocedal and Wright (2nd edition) (sec.
7.2).
In addition, LBFGS supports preconditioning via the P and
precondprep keywords.
Description
=============
The LBFGS method implements the limited-memory BFGS
algorithm as described in Nocedal and Wright (sec. 7.2,
2006) and original paper by Liu & Nocedal (1989). It is a
quasi-Newton method that updates an approximation to the
Hessian using past approximations as well as the gradient.
References
============
β’ Wright, S. J. and J. Nocedal (2006), Numerical
optimization, 2nd edition. Springer
β’ Liu, D. C. and Nocedal, J. (1989). "On the
Limited Memory Method for Large Scale
Optimization". Mathematical Programming B. 45
(3): 503β528
Documentation
For more details and options, see the documentation
- STABLE β most recently tagged version of the documentation.
- LATEST β in-development version of the documentation.
Installation
The package is a registered package, and can be installed with Pkg.add.
julia> using Pkg; Pkg.add("Optim")or through the pkg REPL mode by typing
] add Optim
Citation
If you use Optim.jl in your work, please cite the following.
@article{mogensen2018optim,
author = {Mogensen, Patrick Kofod and Riseth, Asbj{\o}rn Nilsen},
title = {Optim: A mathematical optimization package for {Julia}},
journal = {Journal of Open Source Software},
year = {2018},
volume = {3},
number = {24},
pages = {615},
doi = {10.21105/joss.00615}
}