Convex219.jl

using Mosek
using SCS
import DSP: conv
using Convex
conv(x::AbstractVector, y::AbstractVector) = DSP.conv(x,y)
conv(x::Variable, y::AbstractVector) = Convex.conv(x,y)
conv(x::AbstractVector, y::Variable) = Convex.conv(x,y)

using Random
using SparseArrays

Random.seed!(123)
println(" \n \n \n solving Convex \n \n \n")
n,m = 100, 10
h = randn(n)
x = Vector(sprandn(m, 0.05))
y = conv(h,x)+randn(n+m-1)
lambda = 0.01

x0 = Variable(m)
# slv = Mosek.Optimizer()
slv = SCS.Optimizer(verbose=0)
problem = minimize(0.5*square(norm(conv(h,x0)-y))+lambda*norm(x0,1))
solve!(problem, slv)
@show x0.value
xConvex = x0.value


println(" \n \n \n solving cvxpy \n \n \n")
using PyCall
# Conda.add("cvxpy"; channel="conda-forge")
@pyimport cvxpy as cvx

slv = cvx.SCS
x0 = cvx.Variable(m)
yy = reshape(y, (length(y), 1))
problem = cvx.Problem(cvx.Minimize(cvx.sum_squares(cvx.conv(h,x0)-yy)*0.5+cvx.norm1(x0)*lambda))
problem.solve(solver = slv, verbose = true)

xcvxpy = x0.value

norm(xcvxpy-xConvex)

Note: this was updated for Convex 0.13 in the second revision, so go to the first revision for the Convex 0.12 version. Also, uncomment the Conda.add command (and do using Conda) to install cvxpy if it's not already installed.