Different results when using Jump wrapper and scs_solve #304
Description
The testing code are:
function test()
rng = Random.MersenneTwister(1)
m = 3
n = 1
u = rand(rng, m, n)
w = rand(rng, m)
btilde = rand(rng, n)
######## generate data ########
b = zeros(m * n + m + n + 3m)
b[1:n] .= btilde
for i in 1:m
# b[m * n + n + 3(i - 1) + 2] = -1.0
b[m * n + n + m + 3(i - 1) + 2] = -1.0
end
u = vec(u')
sparse_u = sparse(u)
nnz_u = nnz(sparse_u)
println(nnz_u)
row_indices = zeros(Int, nnz_u)
for i = 1:nnz_u
row_indices[i] = (sparse_u.nzind[i] - 1) ÷ n + 1 + n
end
c = zeros(m*n + 2*m)
@views c[m*n+1:2:m*n+2*m-1] .= -w
row1 = 1:(m * n)
row1 = row1 .+ n .+ m
col1 = 1:(m * n)
val1 = fill(1.0, m * n)
rows = repeat(1:n, m)
cols = repeat((0:(m-1)) * n, inner=n) .+ repeat(1:n, m)
values = ones(n * m)
rows = vcat([rows, row1]...)
cols = vcat([cols, col1]...)
val = vcat([values, val1]...)
row2 = row_indices
col2 = sparse_u.nzind
val2 = -sparse_u.nzval
row = vcat([rows, row2]...)
col = vcat([cols, col2]...)
val = vcat([val, val2]...)
row3 = (n+1) : (n+m)
row3 = row3
col3 = m * n .+ 2 .* (1:m) .- 1
val3 = fill(1.0, m)
row = vcat([row, row3]...)
col = vcat([col, col3]...)
val = vcat([val, val3]...)
row4 = vcat([[3*i + 1, 3i+3] for i in 0:(m-1)]...) .+ (m + n)
row4 = row4 .+ (n * m)
col4 = Vector{Integer}(1:2m)
col4 = col4 .+ (m * n)
val4 = fill(1.0, 2m)
row = vcat([row, row4]...)
col = vcat([col, col4]...)
val = vcat([val, val4]...)
A = sparse(row, col, val, m + n + 3m + m *n, m*n + m + m)
A = SparseMatrixCSC(A)
mA, nA = size(A)
######### solve with scs #########
model = Model(SCS.Optimizer)
@variable(model, x[1:nA])
@objective(model, Min, c' * x)
@constraint(model, A[1:m+n, :] * x .== b[1:m+n]) # 1:m+n
@constraint(model, A[m+n+1:m+n+m*n, :] * x .>= b[m+n+1:m+n+m*n]) # m+n+1:m+n+m*n
@constraint(model, con[i=1:m], [A[m+n+m*n+3(i-1)+1, :]' * x - b[m+n+m*n+3(i-1)+1], A[m+n+m*n+3(i-1)+2, :]' * x - b[m+n+m*n+3(i-1)+2], A[m+n+m*n+3(i-1)+3, :]' * x - b[m+n+m*n+3(i-1)+3]] in MOI.ExponentialCone())
# @constraint(model, con[i=1:m], [x[m*n + 2*i - 1], 1.0, x[m*n + 2*i]] in MOI.ExponentialCone())
optimize!(model)
println("objective_value: ", objective_value(model))
println("x: ", value.(x))
println("outer A.nzval: ", A.nzval)
println("outer A.rowval: ", A.rowval)
println("outer A.colptr: ", A.colptr)
sol_res = SCS.scs_solve(
SCS.DirectSolver,
mA,
nA,
A,
sparse(zeros(nA, nA)),
-b,
c,
m + n, # z
m * n, # l
Float64[], # bu
Float64[], # bl
Vector{Integer}([]), # q
Vector{Integer}([]), # s
m,
0,
Float64[],
zeros(nA),
zeros(mA),
zeros(mA)
)
end
test()The results between JUMP api and scs_solve are different. What is the reason?
------------------------------------------------------------------
SCS v3.2.7 - Splitting Conic Solver
(c) Brendan O'Donoghue, Stanford University, 2012
------------------------------------------------------------------
problem: variables n: 9, constraints m: 16
cones: z: primal zero / dual free vars: 4
l: linear vars: 3
e: exp vars: 9, dual exp vars: 0
settings: eps_abs: 1.0e-04, eps_rel: 1.0e-04, eps_infeas: 1.0e-07
alpha: 1.50, scale: 1.00e-01, adaptive_scale: 1
max_iters: 100000, normalize: 1, rho_x: 1.00e-06
acceleration_lookback: 10, acceleration_interval: 10
compiled with openmp parallelization enabled
lin-sys: sparse-direct-amd-qdldl
nnz(A): 18, nnz(P): 0
------------------------------------------------------------------
iter | pri res | dua res | gap | obj | scale | time (s)
------------------------------------------------------------------
0| 9.54e-01 5.04e-01 6.93e-01 -5.54e-02 1.00e-01 2.35e-03
50| 2.15e-04 1.44e-05 7.30e-05 -1.61e-01 1.00e-01 4.52e-03
------------------------------------------------------------------
status: solved
timings: total: 4.52e-03s = setup: 1.42e-04s + solve: 4.38e-03s
lin-sys: 1.46e-05s, cones: 4.22e-03s, accel: 1.37e-06s
------------------------------------------------------------------
objective = -0.161192
------------------------------------------------------------------
objective_value: -0.16122833996512112
x: [-0.00020622095726905562, 0.9523381209761298, -0.00021521556977977655, -4.870661351048371e-5, 1.7127410306943451, 0.3300014342567794, 3.072837080661251, -6.735386102597836e-5, 1.8484621613426016]
outer A.nzval: [1.0, -0.23603334566204692, 1.0, 1.0, -0.34651701419196046, 1.0, 1.0, -0.3127069683360675, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0]
outer A.rowval: [1, 2, 5, 1, 3, 6, 1, 4, 7, 2, 8, 10, 3, 11, 13, 4, 14, 16]
outer A.colptr: [1, 4, 7, 10, 12, 13, 15, 16, 18, 19]
------------------------------------------------------------------
SCS v3.2.7 - Splitting Conic Solver
(c) Brendan O'Donoghue, Stanford University, 2012
------------------------------------------------------------------
problem: variables n: 9, constraints m: 16
cones: z: primal zero / dual free vars: 4
l: linear vars: 3
e: exp vars: 9, dual exp vars: 0
settings: eps_abs: 1.0e-04, eps_rel: 1.0e-04, eps_infeas: 1.0e-07
alpha: 1.50, scale: 1.00e-01, adaptive_scale: 1
max_iters: 100000, normalize: 1, rho_x: 1.00e-06
acceleration_lookback: 10, acceleration_interval: 10
compiled with openmp parallelization enabled
lin-sys: sparse-direct-amd-qdldl
nnz(A): 18, nnz(P): 0
------------------------------------------------------------------
iter | pri res | dua res | gap | obj | scale | time (s)
------------------------------------------------------------------
0| 9.58e-01 3.74e-01 6.80e-01 2.30e-01 1.00e-01 1.38e-04
50| 2.94e-04 6.04e-05 5.47e-06 1.71e-03 1.00e-01 2.62e-03
------------------------------------------------------------------
status: solved
timings: total: 2.62e-03s = setup: 2.42e-05s + solve: 2.60e-03s
lin-sys: 1.99e-05s, cones: 2.42e-03s, accel: 1.74e-06s
------------------------------------------------------------------
objective = 0.001712
------------------------------------------------------------------