Optimization.jl
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
OptimizationBase in the standard way:
using Pkg
Pkg.add("OptimizationBase")
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:
Tutorials and Documentation
For information on using the package,
see the stable documentation. Use the
in-development documentation for the version of
the documentation, which contains the unreleased features.
Examples
using OptimizationBase
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())
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:
using ForwardDiff, ADTypes
f = OptimizationFunction(rosenbrock, ADTypes.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
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.
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