Try to keep a reference to permutation

lib/MadNLPGPU/src/cudss.jl

@@ -5,6 +5,7 @@ import SparseArrays
     # Use LDLᵀ by default in CUDSS as Cholesky can lead to undefined behavior.
     cudss_algorithm::MadNLP.LinearFactorization = MadNLP.LDL
     ordering::ORDERING = DEFAULT_ORDERING
+    permutation::Vector{Cint} = Cint[]
 end
 
 mutable struct CUDSSSolver{T} <: MadNLP.AbstractLinearSolver{T}
@@ -49,15 +50,16 @@ function CUDSSSolver(
         if opt.ordering == AMD_ORDERING
             A = SparseMatrixCSC(csc)
             G = Metis.graph(A, check_hermitian=false)
-            perm, iperm = Metis.permutation(G)
-            cudss_set(solver, "user_perm", perm)
+            opt.perm, _ = Metis.permutation(G)
         elseif opt.ordering == METIS_ORDERING
             A = SparseMatrixCSC(csc)
-            perm = AMD.amd(A)
-            cudss_set(solver, "user_perm", perm)
+            opt.perm = AMD.amd(A)
+        elseif opt.ordering == USER_ORDERING
+            (!isempty(opt.perm) && isperm(opt.perm)) || error("The vector opt.perm is not a valable permutation.")
         else
             error("The ordering $(opt.ordering) is not supported.")
         end
+        cudss_set(solver, "user_perm", opt.perm)
     end
 
     x_gpu = CUDA.zeros(T, n)

lib/MadNLPGPU/src/cusolverrf.jl

@@ -185,6 +185,7 @@ MadNLP.introduce(M::GLUSolver) = "GLU"
     DEFAULT_ORDERING = 0
     METIS_ORDERING = 1
     AMD_ORDERING = 2
+    USER_ORDERING = 3
 end
 @kwdef mutable struct CuCholeskySolverOptions <: MadNLP.AbstractOptions
     ordering::ORDERING = METIS_ORDERING