Basic usage

In this tutorial we introduce the basics of GalcticOptim.jl by showing how to easily mix local optimizers from Optim.jl and global optimizers from BlackBoxOptim.jl on the Rosenbrock equation. The simplest copy-pasteable code to get started is the following:

 using GalacticOptim, Optim
 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)
 sol = solve(prob,NelderMead())


 using BlackBoxOptim
 prob = OptimizationProblem(rosenbrock, x0, p, lb = [-1.0,-1.0], ub = [1.0,1.0])
 sol = solve(prob,BBO())

Note that Optim.jl is a core dependency of GalaticOptim.jl. However, BlackBoxOptim.jl is not and must already be installed (see the list above).

Warning: The output of the second optimization task (BBO()) 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:

 f = OptimizationFunction(rosenbrock, GalacticOptim.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 GalacticOptim.jl provides an intuitive way of specifying optimization tasks and offers a relatively easy access to a wide range of optimization algorithms.