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https://github.com/julianlsolvers/optim.jl
Optimization functions for Julia
https://github.com/julianlsolvers/optim.jl
julia optim optimisation optimization unconstrained-optimisation unconstrained-optimization
Last synced: about 21 hours ago
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Optimization functions for Julia
- Host: GitHub
- URL: https://github.com/julianlsolvers/optim.jl
- Owner: JuliaNLSolvers
- License: other
- Created: 2012-04-04T22:19:35.000Z (over 12 years ago)
- Default Branch: master
- Last Pushed: 2024-10-29T09:38:09.000Z (22 days ago)
- Last Synced: 2024-10-29T09:46:36.043Z (22 days ago)
- Topics: julia, optim, optimisation, optimization, unconstrained-optimisation, unconstrained-optimization
- Language: Julia
- Homepage:
- Size: 5.82 MB
- Stars: 1,124
- Watchers: 33
- Forks: 220
- Open Issues: 104
-
Metadata Files:
- Readme: README.md
- Changelog: NEWS.md
- Contributing: CONTRIBUTING.md
- License: LICENSE.md
- Citation: CITATION.bib
Awesome Lists containing this project
README
# Optim.jl
[](https://julianlsolvers.github.io/Optim.jl/stable)
[](https://julianlsolvers.github.io/Optim.jl/dev)
[](https://github.com/JuliaNLSolvers/Optim.jl/actions/workflows/CI.yml?query=branch%3Amaster)
[](https://codecov.io/gh/JuliaNLSolvers/Optim.jl)
[](https://doi.org/10.21105/joss.00615)
Univariate and multivariate optimization in Julia.
Optim.jl is part of the [JuliaNLSolvers](https://github.com/JuliaNLSolvers)
family.
## Help and support
For help and support, please post on the [Optimization (Mathematical)](https://discourse.julialang.org/c/domain/opt/13)
section of the Julia discourse or the `#math-optimization` channel of the Julia [slack](https://julialang.org/slack/).
## Installation
Install `Optim.jl` using the Julia package manager:
```julia
import Pkg
Pkg.add("Optim")
```
## Documentation
The online documentation is available at [https://julianlsolvers.github.io/Optim.jl/stable](https://julianlsolvers.github.io/Optim.jl/stable).
## Example
To minimize the [Rosenbrock function](https://en.wikipedia.org/wiki/Rosenbrock_function),
do:
```julia
julia> using Optim
julia> rosenbrock(x) = (1.0 - x[1])^2 + 100.0 * (x[2] - x[1]^2)^2
rosenbrock (generic function with 1 method)
julia> result = optimize(rosenbrock, zeros(2), BFGS())
* Status: success
* Candidate solution
Final objective value: 5.471433e-17
* Found with
Algorithm: BFGS
* Convergence measures
|x - x'| = 3.47e-07 ≰ 0.0e+00
|x - x'|/|x'| = 3.47e-07 ≰ 0.0e+00
|f(x) - f(x')| = 6.59e-14 ≰ 0.0e+00
|f(x) - f(x')|/|f(x')| = 1.20e+03 ≰ 0.0e+00
|g(x)| = 2.33e-09 ≤ 1.0e-08
* Work counters
Seconds run: 0 (vs limit Inf)
Iterations: 16
f(x) calls: 53
∇f(x) calls: 53
julia> Optim.minimizer(result)
2-element Vector{Float64}:
0.9999999926033423
0.9999999852005355
julia> Optim.minimum(result)
5.471432670590216e-17
```
To get information on the keywords used to construct method instances, use the
Julia REPL help prompt (`?`)
```julia
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): 503–528
```
## Use with JuMP
You can use Optim.jl with [JuMP.jl](https://github.com/jump-dev/JuMP.jl) as
follows:
```julia
julia> using JuMP, Optim
julia> model = Model(Optim.Optimizer);
julia> set_optimizer_attribute(model, "method", BFGS())
julia> @variable(model, x[1:2]);
julia> @objective(model, Min, (1.0 - x[1])^2 + 100.0 * (x[2] - x[1]^2)^2)
(x[1]² - 2 x[1] + 1) + (100.0 * ((-x[1]² + x[2]) ^ 2.0))
julia> optimize!(model)
julia> objective_value(model)
3.7218241804173566e-21
julia> value.(x)
2-element Vector{Float64}:
0.9999999999373603
0.99999999986862
```
## 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}
}
```