diff --git a/src/Optimization.jl b/src/Optimization.jl
index 4cfeead6e..8d0257dd1 100644
--- a/src/Optimization.jl
+++ b/src/Optimization.jl
@@ -24,6 +24,7 @@ include("utils.jl")
 include("state.jl")
 include("lbfgsb.jl")
 include("sophia.jl")
+include("auglag.jl")
 
 export solve
 
diff --git a/src/auglag.jl b/src/auglag.jl
new file mode 100644
index 000000000..390659c8e
--- /dev/null
+++ b/src/auglag.jl
@@ -0,0 +1,179 @@
+@kwdef struct AugLag
+    inner
+    τ = 0.5
+    γ = 10.0
+    λmin = -1e20
+    λmax = 1e20
+    μmin = 0.0
+    μmax = 1e20
+    ϵ = 1e-8
+end
+
+SciMLBase.supports_opt_cache_interface(::AugLag) = true
+SciMLBase.allowsbounds(::AugLag) = true
+SciMLBase.requiresgradient(::AugLag) = true
+SciMLBase.allowsconstraints(::AugLag) = true
+SciMLBase.requiresconsjac(::AugLag) = true
+
+function __map_optimizer_args(cache::Optimization.OptimizationCache, opt::AugLag;
+        callback = nothing,
+        maxiters::Union{Number, Nothing} = nothing,
+        maxtime::Union{Number, Nothing} = nothing,
+        abstol::Union{Number, Nothing} = nothing,
+        reltol::Union{Number, Nothing} = nothing,
+        verbose::Bool = false,
+        kwargs...)
+    if !isnothing(abstol)
+        @warn "common abstol is currently not used by $(opt)"
+    end
+    if !isnothing(maxtime)
+        @warn "common abstol is currently not used by $(opt)"
+    end
+
+    mapped_args = (;)
+
+    if cache.lb !== nothing && cache.ub !== nothing
+        mapped_args = (; mapped_args..., lb = cache.lb, ub = cache.ub)
+    end
+
+    if !isnothing(maxiters)
+        mapped_args = (; mapped_args..., maxiter = maxiters)
+    end
+
+    if !isnothing(reltol)
+        mapped_args = (; mapped_args..., pgtol = reltol)
+    end
+
+    return mapped_args
+end
+
+function SciMLBase.__solve(cache::OptimizationCache{
+        F,
+        RC,
+        LB,
+        UB,
+        LC,
+        UC,
+        S,
+        O,
+        D,
+        P,
+        C
+}) where {
+        F,
+        RC,
+        LB,
+        UB,
+        LC,
+        UC,
+        S,
+        O <:
+        AugLag,
+        D,
+        P,
+        C
+}
+maxiters = Optimization._check_and_convert_maxiters(cache.solver_args.maxiters)
+
+local x
+
+solver_kwargs = __map_optimizer_args(cache, cache.opt; maxiters, cache.solver_args...)
+
+if !isnothing(cache.f.cons)
+    eq_inds = [cache.lcons[i] == cache.ucons[i] for i in eachindex(cache.lcons)]
+    ineq_inds = (!).(eq_inds)
+
+    τ = cache.opt.τ
+    γ = cache.opt.γ
+    λmin = cache.opt.λmin
+    λmax = cache.opt.λmax
+    μmin = cache.opt.μmin
+    μmax = cache.opt.μmax
+    ϵ = cache.opt.ϵ
+
+    λ = zeros(eltype(cache.u0), sum(eq_inds))
+    μ = zeros(eltype(cache.u0), sum(ineq_inds))
+
+    cons_tmp = zeros(eltype(cache.u0), length(cache.lcons))
+    cache.f.cons(cons_tmp, cache.u0)
+    ρ = max(1e-6, min(10, 2 * (abs(cache.f(cache.u0, iterate(cache.p)[1]))) / norm(cons_tmp)))
+
+    _loss = function (θ, p = cache.p)
+        x = cache.f(θ, p)
+        cons_tmp .= zero(eltype(θ))
+        cache.f.cons(cons_tmp, θ)
+        cons_tmp[eq_inds] .= cons_tmp[eq_inds] - cache.lcons[eq_inds]
+        cons_tmp[ineq_inds] .= cons_tmp[ineq_inds] .- cache.ucons[ineq_inds]
+        opt_state = Optimization.OptimizationState(u = θ, objective = x[1])
+        if cache.callback(opt_state, x...)
+            error("Optimization halted by callback.")
+        end
+        return x[1] + sum(@. λ * cons_tmp[eq_inds] + ρ / 2 * (cons_tmp[eq_inds] .^ 2)) +
+               1 / (2 * ρ) * sum((max.(Ref(0.0), μ .+ (ρ .* cons_tmp[ineq_inds]))) .^ 2)
+    end
+
+    prev_eqcons = zero(λ)
+    θ = cache.u0
+    β = max.(cons_tmp[ineq_inds], Ref(0.0))
+    prevβ = zero(β)
+    eqidxs = [eq_inds[i] > 0 ? i : nothing for i in eachindex(ineq_inds)]
+    ineqidxs = [ineq_inds[i] > 0 ? i : nothing for i in eachindex(ineq_inds)]
+    eqidxs = eqidxs[eqidxs .!= nothing]
+    ineqidxs = ineqidxs[ineqidxs .!= nothing]
+    function aug_grad(G, θ, p)
+        cache.f.grad(G, θ, p)
+        if !isnothing(cache.f.cons_jac_prototype)
+            J = Float64.(cache.f.cons_jac_prototype)
+        else
+            J = zeros((length(cache.lcons), length(θ)))
+        end
+        cache.f.cons_j(J, θ)
+        __tmp = zero(cons_tmp)
+        cache.f.cons(__tmp, θ)
+        __tmp[eq_inds] .= __tmp[eq_inds] .- cache.lcons[eq_inds]
+        __tmp[ineq_inds] .= __tmp[ineq_inds] .- cache.ucons[ineq_inds]
+        G .+= sum(
+            λ[i] .* J[idx, :] + ρ * (__tmp[idx] .* J[idx, :])
+            for (i, idx) in enumerate(eqidxs);
+            init = zero(G)) #should be jvp
+        G .+= sum(
+            1 / ρ * (max.(Ref(0.0), μ[i] .+ (ρ .* __tmp[idx])) .* J[idx, :])
+            for (i, idx) in enumerate(ineqidxs);
+            init = zero(G)) #should be jvp
+    end
+
+    opt_ret = ReturnCode.MaxIters
+    n = length(cache.u0)
+
+    augprob = OptimizationProblem(OptimizationFunction(_loss; grad = aug_grad), cache.u0, cache.p)
+
+    solver_kwargs = Base.structdiff(solver_kwargs, (; lb = nothing, ub = nothing))
+
+    for i in 1:(maxiters/10)
+        prev_eqcons .= cons_tmp[eq_inds] .- cache.lcons[eq_inds]
+        prevβ .= copy(β)
+        res = solve(augprob, cache.opt.inner, maxiters = maxiters / 10)
+        θ = res.u
+        cons_tmp .= 0.0
+        cache.f.cons(cons_tmp, θ)
+        λ = max.(min.(λmax, λ .+ ρ * (cons_tmp[eq_inds] .- cache.lcons[eq_inds])), λmin)
+        β = max.(cons_tmp[ineq_inds], -1 .* μ ./ ρ)
+        μ = min.(μmax, max.(μ .+ ρ * cons_tmp[ineq_inds], μmin))
+        if max(norm(cons_tmp[eq_inds] .- cache.lcons[eq_inds], Inf), norm(β, Inf)) >
+           τ * max(norm(prev_eqcons, Inf), norm(prevβ, Inf))
+            ρ = γ * ρ
+        end
+        if norm(
+            (cons_tmp[eq_inds] .- cache.lcons[eq_inds]) ./ cons_tmp[eq_inds], Inf) <
+           ϵ && norm(β, Inf) < ϵ
+            opt_ret = ReturnCode.Success
+            break
+        end
+    end
+    stats = Optimization.OptimizationStats(; iterations = maxiters,
+            time = 0.0, fevals = maxiters, gevals = maxiters)
+    return SciMLBase.build_solution(
+            cache, cache.opt, θ, x,
+            stats = stats, retcode = opt_ret)
+end
+end
\ No newline at end of file
diff --git a/src/lbfgsb.jl b/src/lbfgsb.jl
index 514b20666..f3d3c79c7 100644
--- a/src/lbfgsb.jl
+++ b/src/lbfgsb.jl
@@ -45,7 +45,7 @@ function __map_optimizer_args(cache::Optimization.OptimizationCache, opt::LBFGS;
         @warn "common abstol is currently not used by $(opt)"
     end
     if !isnothing(maxtime)
-        @warn "common abstol is currently not used by $(opt)"
+        @warn "common maxtime is currently not used by $(opt)"
     end
 
     mapped_args = (;)
diff --git a/test/lbfgsb.jl b/test/lbfgsb.jl
index 2b5ec1691..b981cc2f2 100644
--- a/test/lbfgsb.jl
+++ b/test/lbfgsb.jl
@@ -25,3 +25,31 @@ prob = OptimizationProblem(optf, x0, lcons = [1.0, -Inf],
     ub = [1.0, 1.0])
 @time res = solve(prob, Optimization.LBFGS(), maxiters = 100)
 @test res.retcode == SciMLBase.ReturnCode.Success
+
+using MLUtils, OptimizationOptimisers
+
+x0 = -pi:0.001:pi
+y0 = sin.(x0)
+data = MLUtils.DataLoader((x0, y0), batchsize = 100)
+function loss(coeffs, data)
+    ypred = [evalpoly(data[1][i], coeffs) for i in eachindex(data[1])]
+    return sum(abs2, ypred .- data[2])
+end
+
+function cons1(res, coeffs, p = nothing)
+    res[1] = coeffs[1] * coeffs[5] - 1
+    return nothing
+end
+
+optf = OptimizationFunction(loss, AutoSparseForwardDiff(), cons = cons1)
+callback = (st, l) -> (@show l; return false)
+
+prob = OptimizationProblem(optf, rand(5), (x0, y0), lcons = [-0.5], ucons = [0.5], lb = [-10.0, -10.0, -10.0, -10.0, -10.0], ub = [10.0, 10.0, 10.0, 10.0, 10.0])
+opt1 = solve(prob, Optimization.LBFGS(), maxiters = 1000, callback = callback)
+
+prob = OptimizationProblem(optf, rand(5), data, lcons = [0.0], ucons = [0.0], lb = [-10.0, -10.0, -10.0, -10.0, -10.0], ub = [10.0, 10.0, 10.0, 10.0, 10.0])
+opt = solve(prob, Optimization.AugLag(; inner = Adam()), maxiters = 500, callback = callback)
+
+optf1 = OptimizationFunction(loss, AutoSparseForwardDiff())
+prob1 = OptimizationProblem(optf1, rand(5), data)
+sol1 = solve(prob1, OptimizationOptimisers.Adam(), maxiters = 1000, callback = callback)