StructuredOptimization.jl

StructuredOptimization.jl is a high-level modeling language that utilizes a syntax that is very close to the mathematical formulation of an optimization problem.

This user-friendly interface acts as a parser to utilize three different packages:

• ProximalOperators.jl

• AbstractOperators.jl

• ProximalAlgorithms.jl

StructuredOptimization.jl can handle large-scale convex and nonconvex problems with nonsmooth cost functions.

It supports complex variables as well.

To install the package, hit ] from the Julia command line to enter the package manager, then

pkg> add StructuredOptimization

A least absolute shrinkage and selection operator (LASSO) can be solved with only few lines of code:

julia> using StructuredOptimization

julia> n, m = 100, 10;                # define problem size

julia> A, y = randn(m,n), randn(m);   # random problem data

julia> x = Variable(n);               # initialize optimization variable

julia> λ = 1e-2*norm(A'*y,Inf);       # define λ    

julia> @minimize ls( A*x - y ) + λ*norm(x, 1); # solve problem

julia> ~x                             # inspect solution
100-element Array{Float64,1}:
  0.0
  0.0
  0.0
  0.440254
  0.0
  0.0
  0.0
[...]

See the documentation for more details about the type of problems StructuredOptimization.jl can handle and the demos to check out some examples.