diff --git a/lib/OptimizationBase/ext/OptimizationZygoteExt.jl b/lib/OptimizationBase/ext/OptimizationZygoteExt.jl
index 461efe699..1e26909af 100644
--- a/lib/OptimizationBase/ext/OptimizationZygoteExt.jl
+++ b/lib/OptimizationBase/ext/OptimizationZygoteExt.jl
@@ -208,7 +208,7 @@ function OptimizationBase.instantiate_function(
         lag_extras = prepare_hessian(
             lagrangian, soadtype, x, Constant(one(eltype(x))),
             Constant(ones(eltype(x), num_cons)), Constant(p), strict = Val(false))
-        lag_hess_prototype = zeros(Bool, num_cons, length(x))
+        lag_hess_prototype = zeros(Bool, length(x), length(x))
 
         function lag_h!(H::AbstractMatrix, θ, σ, λ)
             if σ == zero(eltype(θ))
@@ -288,6 +288,18 @@ function OptimizationBase.instantiate_function(
         f, x, adtype, p, num_cons; kwargs...)
 end
 
+function OptimizationBase.instantiate_function(
+        f::OptimizationFunction{true}, cache::OptimizationBase.ReInitCache,
+        adtype::DifferentiationInterface.SecondOrder{
+            <:ADTypes.AbstractADType, <:ADTypes.AutoZygote},
+        num_cons = 0; kwargs...)
+    x = cache.u0
+    p = cache.p
+
+    return OptimizationBase.instantiate_function(
+        f, x, adtype, p, num_cons; kwargs...)
+end
+
 function OptimizationBase.instantiate_function(
         f::OptimizationFunction{true}, x,
         adtype::ADTypes.AutoSparse{<:Union{ADTypes.AutoZygote,
@@ -575,4 +587,15 @@ function OptimizationBase.instantiate_function(
     return OptimizationBase.instantiate_function(f, x, adtype, p, num_cons; kwargs...)
 end
 
+function OptimizationBase.instantiate_function(
+        f::OptimizationFunction{true}, cache::OptimizationBase.ReInitCache,
+        adtype::ADTypes.AutoSparse{<:DifferentiationInterface.SecondOrder{
+            <:ADTypes.AbstractADType, <:ADTypes.AutoZygote}},
+        num_cons = 0; kwargs...)
+    x = cache.u0
+    p = cache.p
+
+    return OptimizationBase.instantiate_function(f, x, adtype, p, num_cons; kwargs...)
+end
+
 end
diff --git a/lib/OptimizationBase/src/OptimizationDIExt.jl b/lib/OptimizationBase/src/OptimizationDIExt.jl
index adb84b55f..017506a03 100644
--- a/lib/OptimizationBase/src/OptimizationDIExt.jl
+++ b/lib/OptimizationBase/src/OptimizationDIExt.jl
@@ -198,7 +198,7 @@ function instantiate_function(
         lag_prep = prepare_hessian(
             lagrangian, soadtype, x, Constant(one(eltype(x))),
             Constant(ones(eltype(x), num_cons)), Constant(p))
-        lag_hess_prototype = zeros(Bool, num_cons, length(x))
+        lag_hess_prototype = zeros(Bool, length(x), length(x))
 
         function lag_h!(H::AbstractMatrix, θ, σ, λ)
             if σ == zero(eltype(θ))
@@ -457,7 +457,7 @@ function instantiate_function(
         lag_prep = prepare_hessian(
             lagrangian, soadtype, x, Constant(one(eltype(x))),
             Constant(ones(eltype(x), num_cons)), Constant(p))
-        lag_hess_prototype = zeros(Bool, num_cons, length(x))
+        lag_hess_prototype = zeros(Bool, length(x), length(x))
 
         function lag_h!(θ, σ, λ)
             if σ == zero(eltype(θ))
diff --git a/lib/OptimizationBase/src/cache.jl b/lib/OptimizationBase/src/cache.jl
index 375d5aaa1..9454e4f03 100644
--- a/lib/OptimizationBase/src/cache.jl
+++ b/lib/OptimizationBase/src/cache.jl
@@ -62,7 +62,7 @@ function OptimizationCache(prob::SciMLBase.OptimizationProblem, opt;
         g = SciMLBase.requiresgradient(opt), h = SciMLBase.requireshessian(opt),
         hv = SciMLBase.requireshessian(opt), fg = SciMLBase.allowsfg(opt),
         fgh = SciMLBase.allowsfgh(opt), cons_j = SciMLBase.requiresconsjac(opt), cons_h = SciMLBase.requiresconshess(opt),
-        cons_vjp = SciMLBase.allowsconsjvp(opt), cons_jvp = SciMLBase.allowsconsjvp(opt), lag_h = SciMLBase.requireslagh(opt))
+        cons_vjp = SciMLBase.allowsconsvjp(opt), cons_jvp = SciMLBase.allowsconsjvp(opt), lag_h = SciMLBase.requireslagh(opt))
 
     if structural_analysis
         obj_res, cons_res = symify_cache(f, prob, num_cons, manifold)
diff --git a/lib/OptimizationBase/test/adtests.jl b/lib/OptimizationBase/test/adtests.jl
index 6fe4eea05..1a9483deb 100644
--- a/lib/OptimizationBase/test/adtests.jl
+++ b/lib/OptimizationBase/test/adtests.jl
@@ -144,6 +144,17 @@ optprob.cons_h(H3, x0)
     optprob.lag_h(H4, x0, σ, μ)
     @test H4≈σ * H2 + μ[1] * H3[1] rtol=1e-6
 
+    # Test that the AD-generated lag_hess_prototype has correct dimensions
+    @test !isnothing(optprob.lag_hess_prototype)
+    @test size(optprob.lag_hess_prototype) == (length(x0), length(x0))  # Should be n×n, not num_cons×n
+
+    # Test that we can actually use it as a buffer
+    if !isnothing(optprob.lag_hess_prototype)
+        H_proto = similar(optprob.lag_hess_prototype, Float64)
+        optprob.lag_h(H_proto, x0, σ, μ)
+        @test H_proto ≈ σ * H2 + μ[1] * H3[1] rtol=1e-6
+    end
+
     G2 = Array{Float64}(undef, 2)
     H2 = Array{Float64}(undef, 2, 2)
 
@@ -257,6 +268,17 @@ optprob.cons_h(H3, x0)
     optprob.lag_h(H4, x0, σ, μ)
     @test H4≈σ * H2 + μ[1] * H3[1] rtol=1e-6
 
+    # Test that the AD-generated lag_hess_prototype has correct dimensions
+    @test !isnothing(optprob.lag_hess_prototype)
+    @test size(optprob.lag_hess_prototype) == (length(x0), length(x0))  # Should be n×n, not num_cons×n
+
+    # Test that we can actually use it as a buffer (this would fail with the bug)
+    if !isnothing(optprob.lag_hess_prototype)
+        H_proto = similar(optprob.lag_hess_prototype, Float64)
+        optprob.lag_h(H_proto, x0, σ, μ)
+        @test H_proto ≈ σ * H2 + μ[1] * H3[1] rtol=1e-6
+    end
+
     G2 = Array{Float64}(undef, 2)
     H2 = Array{Float64}(undef, 2, 2)
 
@@ -490,6 +512,17 @@ end
     optprob.lag_h(H4, x0, σ, μ)
     @test H4≈σ * H1 + sum(μ .* H3) rtol=1e-6
 
+    # Test that the AD-generated lag_hess_prototype has correct dimensions
+    @test !isnothing(optprob.lag_hess_prototype)
+    @test size(optprob.lag_hess_prototype) == (length(x0), length(x0))  # Should be n×n, not num_cons×n
+
+    # Test that we can actually use it as a buffer (this would fail with the bug)
+    if !isnothing(optprob.lag_hess_prototype)
+        H_proto = similar(optprob.lag_hess_prototype, Float64)
+        optprob.lag_h(H_proto, x0, σ, μ)
+        @test H_proto ≈ σ * H1 + sum(μ .* H3) rtol=1e-6
+    end
+
     G2 = Array{Float64}(undef, 2)
     H2 = Array{Float64}(undef, 2, 2)