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https://github.com/sciml/optimization.jl

Mathematical Optimization in Julia. Local, global, gradient-based and derivative-free. Linear, Quadratic, Convex, Mixed-Integer, and Nonlinear Optimization in one simple, fast, and differentiable interface.
https://github.com/sciml/optimization.jl

algorithmic-differentiation automatic-differentiation convex-optimization derivative-free-optimization global-optimization hacktoberfest julia local-optimization mixed-integer-programming nonlinear-optimization optimization scientific-machine-learning sciml

Last synced: about 1 month ago
JSON representation

Host: GitHub
URL: https://github.com/sciml/optimization.jl
Owner: SciML
License: mit
Created: 2020-05-06T08:00:25.000Z (over 4 years ago)
Default Branch: master
Last Pushed: 2024-04-09T04:45:43.000Z (7 months ago)
Last Synced: 2024-04-14T01:46:58.468Z (7 months ago)
Topics: algorithmic-differentiation, automatic-differentiation, convex-optimization, derivative-free-optimization, global-optimization, hacktoberfest, julia, local-optimization, mixed-integer-programming, nonlinear-optimization, optimization, scientific-machine-learning, sciml
Language: Julia
Homepage: https://docs.sciml.ai/Optimization/stable/
Size: 15.1 MB
Stars: 655
Watchers: 16
Forks: 71
Open Issues: 72
Metadata Files:
- Readme: README.md
- License: LICENSE

Awesome Lists containing this project

README

        # Optimization.jl

[![Join the chat at https://julialang.zulipchat.com #sciml-bridged](https://img.shields.io/static/v1?label=Zulip&message=chat&color=9558b2&labelColor=389826)](https://julialang.zulipchat.com/#narrow/stream/279055-sciml-bridged)

[![Global Docs](https://img.shields.io/badge/docs-SciML-blue.svg)](https://docs.sciml.ai/Optimization/stable/)

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[![DOI](https://zenodo.org/badge/DOI/10.5281/zenodo.7738525.svg)](https://doi.org/10.5281/zenodo.7738525)

Optimization.jl is a package with a scope that is beyond your normal global optimization

package. Optimization.jl seeks to bring together all of the optimization packages

it can find, local and global, into one unified Julia interface. This means, you

learn one package and you learn them all! Optimization.jl adds a few high-level

features, such as integrating with automatic differentiation, to make its usage

fairly simple for most cases, while allowing all of the options in a single

unified interface.

## Installation

Assuming that you already have Julia correctly installed, it suffices to import

Optimization.jl in the standard way:

```julia

using Pkg

Pkg.add("Optimization")

```

The packages relevant to the core functionality of Optimization.jl will be imported

accordingly and, in most cases, you do not have to worry about the manual

installation of dependencies. Below is the list of packages that need to be

installed explicitly if you intend to use the specific optimization algorithms

offered by them:

  - OptimizationBBO for [BlackBoxOptim.jl](https://github.com/robertfeldt/BlackBoxOptim.jl)

  - OptimizationEvolutionary for [Evolutionary.jl](https://github.com/wildart/Evolutionary.jl) (see also [this documentation](https://wildart.github.io/Evolutionary.jl/dev/))

  - OptimizationGCMAES for [GCMAES.jl](https://github.com/AStupidBear/GCMAES.jl)

  - OptimizationMOI for [MathOptInterface.jl](https://github.com/jump-dev/MathOptInterface.jl) (usage of algorithm via MathOptInterface API; see also the API [documentation](https://jump.dev/MathOptInterface.jl/stable/))

  - OptimizationMetaheuristics for [Metaheuristics.jl](https://github.com/jmejia8/Metaheuristics.jl) (see also [this documentation](https://jmejia8.github.io/Metaheuristics.jl/stable/))

  - OptimizationMultistartOptimization for [MultistartOptimization.jl](https://github.com/tpapp/MultistartOptimization.jl) (see also [this documentation](https://juliahub.com/docs/MultistartOptimization/cVZvi/0.1.0/))

  - OptimizationNLopt for [NLopt.jl](https://github.com/JuliaOpt/NLopt.jl) (usage via the NLopt API; see also the available [algorithms](https://nlopt.readthedocs.io/en/latest/NLopt_Algorithms/))

  - OptimizationNOMAD for [NOMAD.jl](https://github.com/bbopt/NOMAD.jl) (see also [this documentation](https://bbopt.github.io/NOMAD.jl/stable/))

  - OptimizationNonconvex for [Nonconvex.jl](https://github.com/JuliaNonconvex/Nonconvex.jl) (see also [this documentation](https://julianonconvex.github.io/Nonconvex.jl/stable/))

  - OptimizationQuadDIRECT for [QuadDIRECT.jl](https://github.com/timholy/QuadDIRECT.jl)

  - OptimizationSpeedMapping for [SpeedMapping.jl](https://github.com/NicolasL-S/SpeedMapping.jl) (see also [this documentation](https://nicolasl-s.github.io/SpeedMapping.jl/stable/))

## Tutorials and Documentation

For information on using the package,

[see the stable documentation](https://docs.sciml.ai/Optimization/stable/). Use the

[in-development documentation](https://docs.sciml.ai/Optimization/dev/) for the version of

the documentation, which contains the unreleased features.

## Examples

```julia

using Optimization

rosenbrock(x, p) = (p[1] - x[1])^2 + p[2] * (x[2] - x[1]^2)^2

x0 = zeros(2)

p = [1.0, 100.0]

prob = OptimizationProblem(rosenbrock, x0, p)

using OptimizationOptimJL

sol = solve(prob, NelderMead())

using OptimizationBBO

prob = OptimizationProblem(rosenbrock, x0, p, lb = [-1.0, -1.0], ub = [1.0, 1.0])

sol = solve(prob, BBO_adaptive_de_rand_1_bin_radiuslimited())

```

Note that Optim.jl is a core dependency of Optimization.jl. However, BlackBoxOptim.jl

is not and must already be installed (see the list above).

*Warning:* The output of the second optimization task (`BBO_adaptive_de_rand_1_bin_radiuslimited()`) is

currently misleading in the sense that it returns `Status: failure (reached maximum number of iterations)`. However, convergence is actually

reached and the confusing message stems from the reliance on the Optim.jl output

struct (where the situation of reaching the maximum number of iterations is

rightly regarded as a failure). The improved output struct will soon be

implemented.

The output of the first optimization task (with the `NelderMead()` algorithm)

is given below:

```

* Status: success

* Candidate solution

   Final objective value:     3.525527e-09

* Found with

   Algorithm:     Nelder-Mead

* Convergence measures

   √(Σ(yᵢ-ȳ)²)/n ≤ 1.0e-08

* Work counters

   Seconds run:   0  (vs limit Inf)

   Iterations:    60

   f(x) calls:    118

```

We can also explore other methods in a similar way:

```julia

using ForwardDiff

f = OptimizationFunction(rosenbrock, Optimization.AutoForwardDiff())

prob = OptimizationProblem(f, x0, p)

sol = solve(prob, BFGS())

```

For instance, the above optimization task produces the following output:

```

* Status: success

* Candidate solution

   Final objective value:     7.645684e-21

* Found with

   Algorithm:     BFGS

* Convergence measures

   |x - x'|               = 3.48e-07 ≰ 0.0e+00

   |x - x'|/|x'|          = 3.48e-07 ≰ 0.0e+00

   |f(x) - f(x')|         = 6.91e-14 ≰ 0.0e+00

   |f(x) - f(x')|/|f(x')| = 9.03e+06 ≰ 0.0e+00

   |g(x)|                 = 2.32e-09 ≤ 1.0e-08

* Work counters

   Seconds run:   0  (vs limit Inf)

   Iterations:    16

   f(x) calls:    53

   ∇f(x) calls:   53

```

```julia

prob = OptimizationProblem(f, x0, p, lb = [-1.0, -1.0], ub = [1.0, 1.0])

sol = solve(prob, Fminbox(GradientDescent()))

```

The examples clearly demonstrate that Optimization.jl provides an intuitive

way of specifying optimization tasks and offers a relatively

easy access to a wide range of optimization algorithms.