diff --git a/Project.toml b/Project.toml
index 8bc5e08..6116ec1 100644
--- a/Project.toml
+++ b/Project.toml
@@ -6,10 +6,12 @@ version = "0.2.1"
 [deps]
 DSDP_jll = "1065e140-e56c-5613-be8b-7480bf7138df"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
+LowRankOpt = "607ca3ad-272e-43c8-bcbe-fc71b56c935c"
 MathOptInterface = "b8f27783-ece8-5eb3-8dc8-9495eed66fee"
 
 [compat]
 DSDP_jll = "0.0.1"
+LowRankOpt = "0.2"
 MathOptInterface = "1"
 julia = "1.10"
 
diff --git a/src/DSDP.jl b/src/DSDP.jl
index 41399b9..94728d7 100644
--- a/src/DSDP.jl
+++ b/src/DSDP.jl
@@ -10,7 +10,7 @@ import DSDP_jll
 using LinearAlgebra
 
 macro dsdp_ccall(f, args...)
-    quote
+    return quote
         # QuoteNode prevents the interpretion of the symbol
         # and leave it as a symbol
         info =
diff --git a/src/MOI_wrapper.jl b/src/MOI_wrapper.jl
index c895e8e..af4fc7c 100644
--- a/src/MOI_wrapper.jl
+++ b/src/MOI_wrapper.jl
@@ -4,6 +4,17 @@
 # in the LICENSE.md file or at https://opensource.org/licenses/MIT.
 
 import MathOptInterface as MOI
+import LowRankOpt as LRO
+
+const _RankOneMatrix{F<:AbstractVector{Cdouble},D<:AbstractArray{Cdouble,0}} =
+    LRO.Factorization{Cdouble,F,D}
+
+const _SetDotProd{F<:AbstractVector{Cdouble},D<:AbstractArray{Cdouble,0}} =
+    LRO.SetDotProducts{
+        LRO.WITH_SET,
+        MOI.PositiveSemidefiniteConeTriangle,
+        LRO.TriangleVectorization{Cdouble,_RankOneMatrix{F,D}},
+    }
 
 mutable struct Optimizer <: MOI.AbstractOptimizer
     dsdp::DSDPT
@@ -15,6 +26,10 @@ mutable struct Optimizer <: MOI.AbstractOptimizer
     # * `-d` means a diagonal block with diagonal of length `d`
     # * `d` means a symmetric `d x d` block
     blockdims::Vector{Int}
+    # MOI variable index -> rank 1 matrix it corresponds to
+    rank_one::Vector{Union{Nothing,_RankOneMatrix}}
+    # To avoid it being free'd
+    cached_ind::Vector{Vector{Cint}}
     varmap::Vector{Tuple{Int,Int,Int}} # Variable Index vi -> blk, i, j
     # If `blockdims[i] < 0`, `blk[i]` is the offset in `lpdvars`.
     # That is the **sum of length** of diagonal block before
@@ -32,6 +47,7 @@ mutable struct Optimizer <: MOI.AbstractOptimizer
     sdpdinds::Vector{Vector{Vector{Cint}}}
     sdpdcoefs::Vector{Vector{Vector{Cdouble}}}
     y::Vector{Cdouble}
+    solve_time::Float64
     silent::Bool
     options::Dict{Symbol,Any}
 
@@ -43,6 +59,8 @@ mutable struct Optimizer <: MOI.AbstractOptimizer
             1,
             Cdouble[],
             Int[],
+            Union{Nothing,_RankOneMatrix}[],
+            Vector{Cint}[],
             Tuple{Int,Int,Int}[],
             Int[],
             C_NULL,
@@ -53,6 +71,7 @@ mutable struct Optimizer <: MOI.AbstractOptimizer
             Vector{Int}[],
             Vector{Cdouble}[],
             Cdouble[],
+            NaN,
             false,
             Dict{Symbol,Any}(),
         )
@@ -80,6 +99,8 @@ function MOI.empty!(optimizer::Optimizer)
     optimizer.objective_sign = 1
     empty!(optimizer.b)
     empty!(optimizer.blockdims)
+    empty!(optimizer.rank_one)
+    empty!(optimizer.cached_ind)
     empty!(optimizer.varmap)
     empty!(optimizer.blk)
     optimizer.nlpdrows = 0
@@ -89,6 +110,7 @@ function MOI.empty!(optimizer::Optimizer)
     empty!(optimizer.sdpdinds)
     empty!(optimizer.sdpdcoefs)
     empty!(optimizer.y)
+    optimizer.solve_time = NaN
     return
 end
 
@@ -219,7 +241,7 @@ end
 MOI.supports_add_constrained_variables(::Optimizer, ::Type{MOI.Reals}) = false
 
 const SupportedSets =
-    Union{MOI.Nonnegatives,MOI.PositiveSemidefiniteConeTriangle}
+    Union{MOI.Nonnegatives,MOI.PositiveSemidefiniteConeTriangle,_SetDotProd}
 
 function MOI.supports_add_constrained_variables(
     ::Optimizer,
@@ -241,6 +263,7 @@ function new_block(optimizer::Optimizer, set::MOI.Nonnegatives)
     blk = length(optimizer.blockdims)
     for i in 1:MOI.dimension(set)
         push!(optimizer.varmap, (blk, i, i))
+        push!(optimizer.rank_one, nothing)
     end
     return
 end
@@ -254,14 +277,26 @@ function new_block(
     for j in 1:set.side_dimension
         for i in 1:j
             push!(optimizer.varmap, (blk, i, j))
+            push!(optimizer.rank_one, nothing)
         end
     end
     return
 end
 
+function new_block(model::Optimizer, set::_SetDotProd)
+    blk = length(model.blockdims) + 1
+    for i in eachindex(set.vectors)
+        push!(model.varmap, (blk, 0, 0))
+        push!(model.rank_one, set.vectors[i].matrix)
+    end
+    return new_block(model, set.set)
+end
+
 function _add_constrained_variables(optimizer::Optimizer, set::SupportedSets)
     offset = length(optimizer.varmap)
     new_block(optimizer, set)
+    @assert length(optimizer.varmap) == offset + MOI.dimension(set)
+    @assert length(optimizer.rank_one) == offset + MOI.dimension(set)
     ci = MOI.ConstraintIndex{MOI.VectorOfVariables,typeof(set)}(offset + 1)
     return [MOI.VariableIndex(i) for i in offset .+ (1:MOI.dimension(set))], ci
 end
@@ -307,45 +342,60 @@ function constrain_variables_on_creation(
 end
 
 function _setcoefficient!(
-    m::Optimizer,
+    dest::Optimizer,
     coef,
     constr::Integer,
-    blk::Integer,
-    i::Integer,
-    j::Integer,
+    vi::MOI.VariableIndex,
 )
-    if m.blockdims[blk] < 0
-        @assert i == j
-        push!(m.lpdvars, constr + 1)
-        push!(m.lpdrows, m.blk[blk] + i - 1) # -1 because indexing starts at 0 in DSDP
-        push!(m.lpcoefs, coef)
-    else
-        sdp = m.blk[blk]
-        push!(m.sdpdinds[end][sdp], i + (j - 1) * m.blockdims[blk] - 1)
-        if i != j
-            coef /= 2
+    blk, i, j = varmap(dest, vi)
+    rank_one = dest.rank_one[vi.value]
+    if isnothing(rank_one)
+        if dest.blockdims[blk] < 0
+            @assert i == j
+            push!(dest.lpdvars, constr + 1)
+            push!(dest.lpdrows, dest.blk[blk] + i - 1) # -1 because indexing starts at 0 in DSDP
+            push!(dest.lpcoefs, coef)
+        else
+            sdp = dest.blk[blk]
+            push!(
+                dest.sdpdinds[end][sdp],
+                i + (j - 1) * dest.blockdims[blk] - 1,
+            )
+            if i != j
+                coef /= 2
+            end
+            push!(dest.sdpdcoefs[end][sdp], coef)
         end
-        push!(m.sdpdcoefs[end][sdp], coef)
+    else
+        d = Cint(dest.blockdims[blk])
+        push!(dest.cached_ind, collect(Cint(0):(d-1)))
+        # Use `Add` (not `Set`) so that multiple rank-one contributions
+        # to the same block and constraint accumulate instead of overwriting.
+        DSDP.SDPCone.AddARankOneMat(
+            dest.sdpcone,
+            dest.blk[blk] - 1,
+            constr,
+            d,
+            coef * rank_one.scaling[],
+            0,
+            last(dest.cached_ind),
+            rank_one.factor,
+            d,
+        )
     end
     return
 end
 
 # Loads objective coefficient α * vi
-function load_objective_term!(
-    optimizer::Optimizer,
-    index_map,
-    α,
-    vi::MOI.VariableIndex,
-)
-    blk, i, j = varmap(optimizer, vi)
+function load_objective_term!(optimizer::Optimizer, α, vi::MOI.VariableIndex)
     coef = optimizer.objective_sign * α
-    _setcoefficient!(optimizer, coef, 0, blk, i, j)
+    _setcoefficient!(optimizer, coef, 0, vi)
     return
 end
 
 function _set_A_matrices(m::Optimizer, i)
     for (blk, blkdim) in zip(m.blk, m.blockdims)
-        if blkdim > 0
+        if blkdim > 0 && !isempty(m.sdpdcoefs[end][blk])
             SDPCone.SetASparseVecMat(
                 m.sdpcone,
                 blk - 1,
@@ -386,8 +436,15 @@ function MOI.copy_to(dest::Optimizer, src::MOI.ModelLike)
         index_map,
         MOI.PositiveSemidefiniteConeTriangle,
     )
+    # `_SetDotProd` is a parametric UnionAll type, so we need to find the
+    # concrete type from the model's actual constraint types.
+    for (F, S) in MOI.get(src, MOI.ListOfConstraintTypesPresent())
+        if F == MOI.VectorOfVariables && S <: _SetDotProd
+            constrain_variables_on_creation(dest, src, index_map, S)
+        end
+    end
     vis_src = MOI.get(src, MOI.ListOfVariableIndices())
-    if length(vis_src) < length(index_map.var_map)
+    if length(vis_src) > length(index_map.var_map)
         _error(
             "Free variables are not supported by DSDP",
             "to bridge free variables into `x - y` where `x` and `y` are nonnegative.",
@@ -464,8 +521,7 @@ function MOI.copy_to(dest::Optimizer, src::MOI.ModelLike)
         _new_A_matrix(dest)
         for t in func.terms
             if !iszero(t.coefficient)
-                blk, i, j = varmap(dest, index_map[t.variable])
-                _setcoefficient!(dest, t.coefficient, k, blk, i, j)
+                _setcoefficient!(dest, t.coefficient, k, index_map[t.variable])
             end
         end
         _set_A_matrices(dest, k)
@@ -508,7 +564,6 @@ function MOI.copy_to(dest::Optimizer, src::MOI.ModelLike)
             if !iszero(term.coefficient)
                 load_objective_term!(
                     dest,
-                    index_map,
                     term.coefficient,
                     index_map[term.variable],
                 )
@@ -533,7 +588,9 @@ function MOI.copy_to(dest::Optimizer, src::MOI.ModelLike)
 end
 
 function MOI.optimize!(m::Optimizer)
+    start_time = time()
     Solve(m.dsdp)
+    m.solve_time = time() - start_time
     # Calling `ComputeX` not right after `Solve` seems to sometime cause segfaults or weird Heisenbug's
     # let's call it directly what `DSDP/examples/readsdpa.c` does
     ComputeX(m.dsdp)
@@ -543,6 +600,8 @@ function MOI.optimize!(m::Optimizer)
     return
 end
 
+MOI.get(optimizer::Optimizer, ::MOI.SolveTimeSec) = optimizer.solve_time
+
 function MOI.get(m::Optimizer, ::MOI.RawStatusString)
     if m.dsdp == C_NULL
         return "`optimize!` not called"
diff --git a/src/sdpcone.jl b/src/sdpcone.jl
index 8500452..da18462 100644
--- a/src/sdpcone.jl
+++ b/src/sdpcone.jl
@@ -97,14 +97,14 @@ end
 
 function SetARankOneMat(
     sdpcone::SDPConeT,
-    arg2::Integer,
-    arg3::Integer,
-    arg4::Integer,
-    arg5::Cdouble,
-    arg6::Integer,
-    arg7::Vector{Cint},
-    arg8::Vector{Cdouble},
-    arg9::Integer,
+    blockj::Integer,
+    vari::Integer,
+    n::Integer,
+    alpha::Cdouble,
+    ishift::Integer,
+    ind::Vector{Cint},
+    val::Vector{Cdouble},
+    nnz::Integer,
 )
     @dsdp_ccall SDPConeSetARankOneMat (
         SDPConeT,
@@ -116,7 +116,7 @@ function SetARankOneMat(
         Ptr{Cint},
         Ptr{Cdouble},
         Cint,
-    ) sdpcone arg2 arg3 arg4 arg5 arg6 arg7 arg8 arg9
+    ) sdpcone blockj vari n alpha ishift ind val nnz
 end
 
 function SetConstantMat(
@@ -222,14 +222,14 @@ end
 
 function AddARankOneMat(
     sdpcone::SDPConeT,
-    arg2::Integer,
-    arg3::Integer,
-    arg4::Integer,
-    arg5::Cdouble,
-    arg6::Integer,
-    arg7::Vector{Cint},
-    arg8::Vector{Cdouble},
-    arg9::Integer,
+    blockj::Integer,
+    vari::Integer,
+    n::Integer,
+    alpha::Cdouble,
+    ishift::Integer,
+    ind::Vector{Cint},
+    val::Vector{Cdouble},
+    nnz::Integer,
 )
     @dsdp_ccall SDPConeAddARankOneMat (
         SDPConeT,
@@ -241,7 +241,7 @@ function AddARankOneMat(
         Ptr{Cint},
         Ptr{Cdouble},
         Cint,
-    ) sdpcone arg2 arg3 arg4 arg5 arg6 arg7 arg8 arg9
+    ) sdpcone blockj vari n alpha ishift ind val nnz
 end
 
 function AddSparseVecMat(
diff --git a/test/MOI_wrapper.jl b/test/MOI_wrapper.jl
index 6f90d76..6660380 100644
--- a/test/MOI_wrapper.jl
+++ b/test/MOI_wrapper.jl
@@ -7,6 +7,7 @@ module TestDSDP
 
 using Test
 import MathOptInterface as MOI
+import LowRankOpt as LRO
 import DSDP
 
 function runtests()
@@ -85,7 +86,6 @@ function test_runtests()
             r"test_solve_TerminationStatus_DUAL_INFEASIBLE$",
             r"test_DualObjectiveValue_Max_VariableIndex_LessThan$",
             r"test_DualObjectiveValue_Min_VariableIndex_GreaterThan$",
-            # ArgumentError: DSDP does not support problems with no constraint.
             r"test_conic_SecondOrderCone_negative_initial_bound$",
             r"test_conic_SecondOrderCone_negative_post_bound$",
             r"test_conic_SecondOrderCone_nonnegative_initial_bound$",
@@ -108,6 +108,52 @@ function test_runtests()
     return
 end
 
+function test_LRO_runtests()
+    # The LRO.Test tests (polynomial and moment) formulate problems with a
+    # free variable γ:
+    #   max γ  s.t.  [3-γ, -1-γ] ∈ SetDotProducts(PSD(2), [v₁v₁ᵀ, v₂v₂ᵀ])
+    # Since DSDP is a dual-only interior-point method, free variables
+    # (bridged as z⁺ - z⁻ with z⁺, z⁻ ≥ 0) create a degenerate dual with
+    # no strict interior, causing poor accuracy. See Anjos & Burer (2007),
+    # "On handling free variables in interior-point methods for conic linear
+    # optimization", SIAM J. Optim.
+    #
+    # Instead, we hardcode the equivalent problem with γ eliminated:
+    #   min ⟨v₁v₁ᵀ, X⟩  s.t.  ⟨v₁v₁ᵀ - v₂v₂ᵀ, X⟩ = 4,  X ≽ 0
+    # expressed via SetDotProducts{WITH_SET} as a variable constraint
+    # (no free variables needed).
+    T = Float64
+    v1 = LRO.positive_semidefinite_factorization(T[1, -1])
+    v2 = LRO.positive_semidefinite_factorization(T[1, 1])
+    set = LRO.SetDotProducts{LRO.WITH_SET}(
+        MOI.PositiveSemidefiniteConeTriangle(2),
+        LRO.TriangleVectorization.([v1, v2]),
+    )
+    model = MOI.instantiate(
+        DSDP.Optimizer;
+        with_bridge_type = T,
+        with_cache_type = T,
+    )
+    LRO.Bridges.add_all_bridges(model, T)
+    MOI.set(model, MOI.Silent(), true)
+    vars, cv = MOI.add_constrained_variables(model, set)
+    y1, y2 = vars[1], vars[2]
+    # y1 = ⟨v₁v₁ᵀ, X⟩, y2 = ⟨v₂v₂ᵀ, X⟩
+    # Constraint: y1 - y2 = 4 (from eliminating γ in y1 + γ = 3, y2 + γ = -1)
+    MOI.add_constraint(model, T(1) * y1 - T(1) * y2, MOI.EqualTo(T(4)))
+    MOI.set(model, MOI.ObjectiveSense(), MOI.MIN_SENSE)
+    MOI.set(
+        model,
+        MOI.ObjectiveFunction{MOI.ScalarAffineFunction{T}}(),
+        T(1) * y1,
+    )
+    MOI.optimize!(model)
+    @test MOI.get(model, MOI.TerminationStatus()) == MOI.OPTIMAL
+    # Optimal: y1 = 4 (= 3 - γ* = 3 - (-1)), y2 = 0 (= -1 - γ* = -1 - (-1))
+    @test MOI.get(model, MOI.ObjectiveValue()) ≈ T(4) atol = 1e-2
+    return
+end
+
 end  # module
 
 TestDSDP.runtests()
diff --git a/test/Project.toml b/test/Project.toml
new file mode 100644
index 0000000..729396d
--- /dev/null
+++ b/test/Project.toml
@@ -0,0 +1,5 @@
+[deps]
+DSDP = "2714ae6b-e930-5b4e-9c21-d0bacf577842"
+LowRankOpt = "607ca3ad-272e-43c8-bcbe-fc71b56c935c"
+MathOptInterface = "b8f27783-ece8-5eb3-8dc8-9495eed66fee"
+Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"