Optimize memory usage in Julia

optimexample.jl

using Optim, NLSolversBase

function datagen(n=5500,k=13)
    b = rand(k)
    l = rand(2)
    x = randn(n,k)
    abil = randn(n,1)
    vabil = randn(n,1)
    sector = 1.0.*(rand(n,1).>0.8)
    weight = rand(n,1)
    y = l[1] .+ l[2].*(x*b .+ abil .+ vabil.^2)
    return y,x,abil,vabil,sector,weight
end
                                        
# Objective function A
function wolslambdaNoAssignCorrFusion(b::Vector,y::Array,x::Array,abil::Array,vabil::Array,sector::Array,weight::Array)
    # λ0 = b[end-1]
    # λ1 = b[end]
    # β  = b[1:end-2]
    
    # sector=1 corresponds to subset of observations that get hit by lambda
    # sector=0 corresponds to all other observations
    
    if ~isequal(size(y),size(sector))
        error("sector variable is wrong")
    end
    
    SSE = sum(weight.*(vabil.*(((sector.==0).*1).+((sector.==1).*b[end-1])).^2 .+ (y.-((sector.==0).*0).-((sector.==1).*b[end-1]).-(((sector.==0).*1).+((sector.==1).*b[end])).*(x*b[1:end-2].+abil)).^2))
    return SSE
end
                                        
                                        
# Objective function B
function wolslambdaNoAssign(b::Vector,y::Array,x::Array,abil::Array,vabil::Array,sector::Array,weight::Array)
    # λ0 = b[end-1]
    # λ1 = b[end]
    # β  = b[1:end-2]
    
    # sector=1 corresponds to subset of observations that get hit by lambda
    # sector=0 corresponds to all other observations
    
    if ~isequal(size(y),size(sector))
        error("sector variable is wrong")
    end
    
    SSE = sum(weight.*(vabil.*(((sector.==0)*1).+((sector.==1)*b[end-1])).^2 .+ (y.-((sector.==0)*0).-((sector.==1)*b[end-1]).-(((sector.==0)*1).+((sector.==1)*b[end])).*(x*b[1:end-2].+abil)).^2))
    return SSE
end
                                        
# Objective function C
function wolslambda(b::Vector,y::Array,x::Array,abil::Array,vabil::Array,sector::Array,weight::Array)
    λ0 = b[end-1]
    λ1 = b[end]
    β  = b[1:end-2]
    
    # sector=1 corresponds to subset of observations that get hit by lambda
    # sector=0 corresponds to all other observations
    
    if ~isequal(size(y),size(sector))
        error("sector variable is wrong")
    end
    
    SSE = sum(weight.*(vabil.*(((sector.==0)*1).+((sector.==1)*λ1)).^2 .+ (y.-((sector.==0)*0).-((sector.==1)*λ0).-(((sector.==0)*1).+((sector.==1)*λ1)).*(x*β.+abil)).^2))
    return SSE
end
                                        
# Objective function D
function wolslambdaNoAssignLooping(b::Vector,y::Array,x::Array,abil::Array,vabil::Array,sector::Array,weight::Array)
    # λ0 = b[end-1]
    # λ1 = b[end]
    # β  = b[1:end-2]
    
    # sector=1 corresponds to subset of observations that get hit by lambda
    # sector=0 corresponds to all other observations
    
    if ~isequal(size(y),size(sector))
        error("sector variable is wrong")
    end

    SSE = 0.0
    for i=1:size(y,1)
        SSE+=weight[i]*(vabil[i]*(((sector[i]==0)*1)+((sector[i]==1)*b[end-1]))^2 + (y[i]-((sector[i]==0)*0)-((sector[i]==1)*b[end-1])-(((sector[i]==0)*1)+((sector[i]==1)*b[end]))*(dot(x[i,:],b[1:end-2])+abil[i]))^2)
    end 

    return SSE
end

# data (arrays):
wageg,xg,abilg,vabilg,gflg,qg = datagen()

bstartg = rand(size(xg,2))
lambdag0start = 0.5
lambdag1start = 0.75

# starting value
x0 = vec([bstartg;lambdag0start;lambdag1start])

fung = TwiceDifferentiable((arg)->wolslambda(arg,wageg,xg,abilg,vabilg,gflg,qg), x0; autodiff = :forward);
println("\n original")
@time res = optimize(fung, x0, LBFGS(), Optim.Options(show_trace=false,iterations=100_000,g_tol=1e-6,f_tol=1e-20))
println(res.minimizer)

fung = TwiceDifferentiable((arg)->wolslambdaNoAssign(arg,wageg,xg,abilg,vabilg,gflg,qg), x0; autodiff = :forward);
println("\n get rid of mutliple copying")
@time res = optimize(fung, x0, LBFGS(), Optim.Options(show_trace=false,iterations=100_000,g_tol=1e-6,f_tol=1e-20))
println(res.minimizer)

fung = TwiceDifferentiable((arg)->wolslambdaNoAssignCorrFusion(arg,wageg,xg,abilg,vabilg,gflg,qg), x0; autodiff = :forward);
println("\n get rid of multiple copying and use correct fusion operators")
@time res = optimize(fung, x0, LBFGS(), Optim.Options(show_trace=false,iterations=100_000,g_tol=1e-6,f_tol=1e-20))
println(res.minimizer)

fung = TwiceDifferentiable((arg)->wolslambdaNoAssignLooping(arg,wageg,xg,abilg,vabilg,gflg,qg), x0; autodiff = :forward);
println("\n loop over observations")
@time res = optimize(fung, x0, LBFGS(), Optim.Options(show_trace=false,iterations=100_000,g_tol=1e-6,f_tol=1e-20))
println(res.minimizer)