diff --git a/src/L2ODLL.jl b/src/L2ODLL.jl
index 93a2dd1..856acec 100644
--- a/src/L2ODLL.jl
+++ b/src/L2ODLL.jl
@@ -178,6 +178,9 @@ end
 function y_shape(cache::DLLCache)
     return length.(get_y_dual(cache.dual_model, cache.decomposition))
 end
+function y_shape(dual_model::JuMP.Model, decomposition::AbstractDecomposition)
+    return length.(get_y_dual(dual_model, decomposition))
+end
 
 """
     flatten_y(y)
diff --git a/src/projection.jl b/src/projection.jl
index f24ef99..f308885 100644
--- a/src/projection.jl
+++ b/src/projection.jl
@@ -32,3 +32,40 @@ function get_y_sets(dual_model, decomposition)
         for set in get_y_constraint(dual_model, decomposition)
     ]
 end
+
+function make_jump_proj_fn(decomposition::AbstractDecomposition, dual_model::JuMP.Model, optimizer; silent=true)
+    sets = get_y_sets(dual_model, decomposition)
+    shapes = y_shape(dual_model, decomposition)
+
+    proj_model = JuMP.Model(optimizer)
+
+    idxs = [(i, ji) for (i,j) in enumerate(shapes) for ji in 1:j]
+    JuMP.@variable(proj_model, y[idxs])
+
+    for (i, set) in enumerate(sets)
+        isnothing(set) && continue
+        y_vars = filter(ij->first(ij)==i, idxs)
+        if length(y_vars) == 1
+            JuMP.@constraint(proj_model, y[only(y_vars)] ∈ set)
+        else
+            JuMP.@constraint(proj_model, y[y_vars] ∈ set)
+        end
+    end
+
+    silent && JuMP.set_silent(proj_model)
+    proj_model.ext[:🔒] = ReentrantLock()
+    # TODO: define frule/rrule using Moreau
+    return (y_prediction) -> begin
+        lock(proj_model.ext[:🔒])
+        try
+            JuMP.set_objective_function(proj_model, sum((y .- flatten_y(y_prediction)).^2))
+            JuMP.set_objective_sense(proj_model, MOI.MIN_SENSE)
+            JuMP.optimize!(proj_model)
+            JuMP.assert_is_solved_and_feasible(proj_model)
+            
+            value.(y)
+        finally
+            unlock(proj_model.ext[:🔒])
+        end
+    end
+end