Optim.jl
========
Univariate and multivariate optimization in Julia.
Optim.jl is part of the [JuliaNLSolvers](https://github.com/JuliaNLSolvers) family.
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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
```julia
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](https://en.wikipedia.org/wiki/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
```jlcon
Results of Optimization Algorithm
* Algorithm: BFGS
* Starting Point: [0.0,0.0]
* Minimizer: [0.9999999926033423,0.9999999852005353]
* Minimum: 5.471433e-17
* Iterations: 16
* Convergence: true
* |x - x'| 0.0e+00: false
|x - x'| = 3.47e-07
* |f(x) - f(x')| 0.0e+00 |f(x)|: false
|f(x) - f(x')| = 1.20e+03 |f(x)|
* |g(x)| 1.0e-08: true
|g(x)| = 2.33e-09
* Stopped by an increasing objective: false
* Reached Maximum Number of Iterations: false
* Objective Calls: 53
* Gradient Calls: 53
```
To get information on the keywords used to construct method instances, use the Julia REPL help prompt (`?`)
```
help?> LBFGS
search: LBFGS
LBFGS
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
============
Wright, S. J. and J. Nocedal (2006), Numerical
optimization, 2nd edition. Springer
Liu, D. C. and Nocedal, J. (1989). "On the
Limited Memory Method for Large Scale
Optimization". Mathematical Programming B. 45
(3): 503528
```
# Documentation
For more details and options, see the documentation
- [STABLE][docs-stable-url] most recently tagged version of the documentation.
- [LATEST][docs-latest-url] in-development version of the documentation.
# Installation
The package is registered in `METADATA.jl` and can be installed with `Pkg.add`.
```julia
julia> Pkg.add("Optim")
```
# Citation
If you use `Optim.jl` in your work, please cite the following.
```tex
@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}
}
```
[docs-latest-img]: https://img.shields.io/badge/docs-latest-blue.svg
[docs-latest-url]: https://julianlsolvers.github.io/Optim.jl/latest
[docs-stable-img]: https://img.shields.io/badge/docs-stable-blue.svg
[docs-stable-url]: https://julianlsolvers.github.io/Optim.jl/stable
[build-img]: https://travis-ci.org/JuliaNLSolvers/Optim.jl.svg?branch=master
[build-url]: https://travis-ci.org/JuliaNLSolvers/Optim.jl
[winbuild-img]: https://ci.appveyor.com/api/projects/status/prp8ygfp4rr9tafe?svg=true
[winbuild-url]: https://ci.appveyor.com/project/blegat/optim-jl
[pkg-0.4-img]: http://pkg.julialang.org/badges/Optim_0.4.svg
[pkg-0.4-url]: http://pkg.julialang.org/?pkg=Optim&ver=0.4
[pkg-0.5-img]: http://pkg.julialang.org/badges/Optim_0.5.svg
[pkg-0.5-url]: http://pkg.julialang.org/?pkg=Optim&ver=0.5
[pkg-0.6-img]: http://pkg.julialang.org/badges/Optim_0.6.svg
[pkg-0.6-url]: http://pkg.julialang.org/?pkg=Optim&ver=0.6
[cov-img]: https://img.shields.io/codecov/c/github/JuliaNLSolvers/Optim.jl/master.svg?maxAge=2592000
[cov-url]: https://codecov.io/gh/JuliaNLSolvers/Optim.jl
[gitter-url]: https://gitter.im/JuliaNLSolvers/Optim.jl
[gitter-img]: https://badges.gitter.im/JuliaNLSolvers/Optim.jl.svg
[zenodo-url]: https://zenodo.org/badge/latestdoi/3933868
[zenodo-img]: https://zenodo.org/badge/3933868.svg
[joss-url]: https://doi.org/10.21105/joss.00615
[joss-img]: http://joss.theoj.org/papers/10.21105/joss.00615/status.svg