diff --git a/benchmark/Project.toml b/benchmark/Project.toml
new file mode 100644
index 0000000..1aa48d6
--- /dev/null
+++ b/benchmark/Project.toml
@@ -0,0 +1,13 @@
+[deps]
+BenchmarkTools = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf"
+CUDA = "052768ef-5323-5732-b1bb-66c8b64840ba"
+ComplementaritySolve = "b40a91a3-bdaf-4e1c-b965-8c278a33a8d3"
+DataFrames = "a93c6f00-e57d-5684-b7b6-d8193f3e46c0"
+NonlinearSolve = "8913a72c-1f9b-4ce2-8d82-65094dcecaec"
+Pkg = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"
+Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
+PyPlot = "d330b81b-6aea-500a-939a-2ce795aea3ee"
+SciMLBenchmarks = "31c91b34-3c75-11e9-0341-95557aab0344"
+StableRNGs = "860ef19b-820b-49d6-a774-d7a799459cd3"
+StatsPlots = "f3b207a7-027a-5e70-b257-86293d7955fd"
+Weave = "44d3d7a6-8a23-5bf8-98c5-b353f8df5ec9"
diff --git a/benchmark/README.md b/benchmark/README.md
new file mode 100644
index 0000000..c129c0b
--- /dev/null
+++ b/benchmark/README.md
@@ -0,0 +1,4 @@
+# ComplementaritySolve.jl Benchmarks
+
+These benchmarks are written using `Weave.jl`, so that we can eventually add them to
+`SciMLBenchmarks.jl`.
diff --git a/benchmark/benchmarks.jl b/benchmark/benchmarks.jl
new file mode 100644
index 0000000..e6137c3
--- /dev/null
+++ b/benchmark/benchmarks.jl
@@ -0,0 +1,19 @@
+using Weave, SciMLBenchmarks
+
+SciMLBenchmarks.repo_directory = joinpath(@__DIR__, "generated")
+
+function findall_jmd_files(dir=@__DIR__)
+    paths = String[]
+    for p in readdir(dir)
+        if isdir(joinpath(dir, p))
+            append!(paths, findall_jmd_files(joinpath(dir, p)))
+        elseif endswith(p, ".jmd")
+            push!(paths, joinpath(dir, p))
+        end
+    end
+    return paths
+end
+
+files = findall_jmd_files()
+
+foreach(f -> SciMLBenchmarks.weave_file(splitdir(f)..., (:script, :github)), files)
diff --git a/benchmark/generated/markdown/lcp/figures/solvers_11_1.png b/benchmark/generated/markdown/lcp/figures/solvers_11_1.png
new file mode 100644
index 0000000..db973bd
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diff --git a/benchmark/generated/markdown/lcp/figures/solvers_13_1.png b/benchmark/generated/markdown/lcp/figures/solvers_13_1.png
new file mode 100644
index 0000000..b9ac946
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diff --git a/benchmark/generated/markdown/lcp/figures/solvers_5_1.png b/benchmark/generated/markdown/lcp/figures/solvers_5_1.png
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diff --git a/benchmark/generated/markdown/lcp/figures/solvers_6_1.png b/benchmark/generated/markdown/lcp/figures/solvers_6_1.png
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diff --git a/benchmark/generated/markdown/lcp/figures/solvers_7_1.png b/benchmark/generated/markdown/lcp/figures/solvers_7_1.png
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diff --git a/benchmark/generated/markdown/lcp/figures/solvers_8_1.png b/benchmark/generated/markdown/lcp/figures/solvers_8_1.png
new file mode 100644
index 0000000..2994a6d
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diff --git a/benchmark/generated/markdown/lcp/solvers.md b/benchmark/generated/markdown/lcp/solvers.md
new file mode 100644
index 0000000..7eb0f0a
--- /dev/null
+++ b/benchmark/generated/markdown/lcp/solvers.md
@@ -0,0 +1,592 @@
+# Benchmarking Available LCP Solvers
+
+
+
+
+## Useful Functions
+
+```julia
+using CUDA, Statistics
+
+CUDA.allowscalar(false)
+
+iscuda(args...) = any(Base.Fix2(isa, CUDA.AnyCuArray), args)
+
+function timer(f, args...; numtimes::Int=10)
+    cuda_mode = iscuda(args...)
+    f(args...) # compile
+    times = zeros(numtimes)
+    for i in eachindex(times)
+        if cuda_mode
+            times[i] = @elapsed CUDA.@sync f(args...)
+        else
+            times[i] = @elapsed f(args...)
+        end
+    end
+    return minimum(times)
+end
+```
+
+```
+timer (generic function with 1 method)
+```
+
+
+
+
+
+## Load Dependencies
+
+```julia
+using BenchmarkTools, ComplementaritySolve, DataFrames, NonlinearSolve, PyPlot, StableRNGs
+```
+
+
+
+
+## Basic LCP
+
+```julia
+A₁ = [2.0 1; 1 2.0]
+q₁ = [-5.0, 6.0]
+```
+
+```
+2-element Vector{Float64}:
+ -5.0
+  6.0
+```
+
+
+
+
+
+### CPU Benchmarks
+
+#### Unbatched Version
+
+```julia
+SOLVERS = [BokhovenIterativeAlgorithm(),
+    PGS(),
+    RPGS(),
+    InteriorPointMethod(),
+    NonlinearReformulation(),
+    NonlinearReformulation(:smooth, Broyden(; batched=true)),
+]
+times = zeros(length(SOLVERS), 2)
+solvers = ["Bok.", "PGS", "RPGS", "IPM", "NLR (Newton)", "NLR (Broyden)"]
+
+for (i, solver) in enumerate(SOLVERS)
+    @info "[CPU] UNBATCHED: Benchmarking $(solvers[i])"
+    prob_iip = LCP{true}(A₁, q₁, rand(StableRNG(0), 2))
+    prob_oop = LCP{false}(A₁, q₁, rand(StableRNG(0), 2))
+    times[i, 1] = timer(solve, prob_iip, solver)
+    times[i, 2] = timer(solve, prob_oop, solver)
+end
+```
+
+
+![](figures/solvers_6_1.png)
+
+
+
+#### Batched Version
+
+Here we are batching the Problem with `N` starting values (typically batching LCPs involves
+batching multiple `M` and `q`)
+
+
+```julia
+SOLVERS = [BokhovenIterativeAlgorithm(Broyden(; batched=true)),
+    PGS(),
+    RPGS(),
+    InteriorPointMethod(),
+    NonlinearReformulation(:smooth, SimpleNewtonRaphson(; batched=true)),
+    NonlinearReformulation(:smooth, SimpleDFSane(; batched=true)),
+    NonlinearReformulation(:smooth, Broyden(; batched=true)),
+]
+BATCH_SIZES = 2 .^ (1:2:11)
+times = zeros(length(SOLVERS), length(BATCH_SIZES), 2)
+solvers = ["Bok.", "PGS", "RPGS", "IPM", "NLR (Newton)", "NLR (DFSane)", "NLR (Broyden)"]
+
+for (i, solver) in enumerate(SOLVERS)
+    @info "[CPU] BATCHED: Benchmarking $(solvers[i])"
+    for (j, N) in enumerate(BATCH_SIZES)
+        prob_iip = LCP{true}(A₁, q₁, rand(StableRNG(0), 2, N))
+        prob_oop = LCP{false}(A₁, q₁, rand(StableRNG(0), 2, N))
+        times[i, j, 2] = timer(solve, prob_oop, solver)
+        if i == 5
+            times[i, j, 1] = -1 # SimpleNewtonRaphson is not implemented for inplace
+            continue
+        end
+        times[i, j, 1] = timer(solve, prob_iip, solver)
+    end
+end
+```
+
+
+![](figures/solvers_8_1.png)
+
+
+
+### CUDA Benchmarks
+
+```julia
+cuA₁ = [2.0 1; 1 2.0] |> cu
+cuq₁ = [-5.0, 6.0] |> cu
+```
+
+```
+2-element CUDA.CuArray{Float32, 1, CUDA.Mem.DeviceBuffer}:
+ -5.0
+  6.0
+```
+
+
+
+
+
+#### Unbatched Version
+
+```julia
+SOLVERS = [BokhovenIterativeAlgorithm(Broyden(; batched=true)),
+    # InteriorPointMethod(),
+    NonlinearReformulation(:smooth, Broyden(; batched=true)),
+]
+times = zeros(length(SOLVERS), 2)
+solvers = ["Bok.", "NLR (Broyden)"]
+
+for (i, solver) in enumerate(SOLVERS)
+    @info "[CUDA] UNBATCHED: Benchmarking $(solvers[i])"
+    prob_iip = LCP{true}(cuA₁, cuq₁, rand(StableRNG(0), 2) |> cu)
+    prob_oop = LCP{false}(cuA₁, cuq₁, rand(StableRNG(0), 2) |> cu)
+    times[i, 1] = timer(solve, prob_iip, solver)
+    times[i, 2] = timer(solve, prob_oop, solver)
+end
+```
+
+
+![](figures/solvers_11_1.png)
+
+
+
+#### Batched Version
+
+
+```julia
+SOLVERS = [BokhovenIterativeAlgorithm(Broyden(; batched=true)),
+    # InteriorPointMethod(),
+    NonlinearReformulation(:smooth, Broyden(; batched=true)),
+]
+BATCH_SIZES = 2 .^ (1:2:11)
+times = zeros(length(SOLVERS), length(BATCH_SIZES), 2)
+solvers = ["Bok.", "NLR (Broyden)"]
+
+for (i, solver) in enumerate(SOLVERS)
+    @info "[CUDA] BATCHED: Benchmarking $(solvers[i])"
+    for (j, N) in enumerate(BATCH_SIZES)
+        prob_iip = LCP{true}(cuA₁, cuq₁, rand(StableRNG(0), 2, N) |> cu)
+        prob_oop = LCP{false}(cuA₁, cuq₁, rand(StableRNG(0), 2, N) |> cu)
+        times[i, j, 2] = timer(solve, prob_oop, solver)
+        times[i, j, 1] = timer(solve, prob_iip, solver)
+    end
+end
+```
+
+
+![](figures/solvers_13_1.png)
+
+
+## Appendix
+
+These benchmarks are a part of the SciMLBenchmarks.jl repository, found at: [https://github.com/SciML/SciMLBenchmarks.jl](https://github.com/SciML/SciMLBenchmarks.jl). For more information on high-performance scientific machine learning, check out the SciML Open Source Software Organization [https://sciml.ai](https://sciml.ai).
+
+To locally run this benchmark, do the following commands:
+
+```
+using SciMLBenchmarks
+SciMLBenchmarks.weave_file("/mnt/research/ComplementaritySolve.jl/benchmark/lcp","solvers.jmd")
+```
+
+Computer Information:
+
+```
+Julia Version 1.9.2
+Commit e4ee485e909 (2023-07-05 09:39 UTC)
+Platform Info:
+  OS: Linux (x86_64-linux-gnu)
+  CPU: 12 × AMD Ryzen 5 4600H with Radeon Graphics
+  WORD_SIZE: 64
+  LIBM: libopenlibm
+  LLVM: libLLVM-14.0.6 (ORCJIT, znver2)
+  Threads: 8 on 12 virtual cores
+Environment:
+  JULIA_PKG_USE_CLI_GIT = true
+  JULIA_DEPOT_PATH = /mnt/julia:
+
+```
+
+Package Information:
+
+```
+Status `/mnt/research/ComplementaritySolve.jl/benchmark/Project.toml`
+  [6e4b80f9] BenchmarkTools v1.3.2
+  [052768ef] CUDA v4.4.0
+  [b40a91a3] ComplementaritySolve v0.1.0 `..`
+  [a93c6f00] DataFrames v1.6.1
+  [8913a72c] NonlinearSolve v1.8.0
+  [91a5bcdd] Plots v1.38.17
+  [d330b81b] PyPlot v2.11.1
+  [31c91b34] SciMLBenchmarks v0.1.3
+  [860ef19b] StableRNGs v1.0.0
+  [f3b207a7] StatsPlots v0.15.6
+  [44d3d7a6] Weave v0.10.12
+  [44cfe95a] Pkg v1.10.0
+```
+
+And the full manifest:
+
+```
+Status `/mnt/research/ComplementaritySolve.jl/benchmark/Manifest.toml`
+  [47edcb42] ADTypes v0.1.6
+  [621f4979] AbstractFFTs v1.4.0
+  [79e6a3ab] Adapt v3.6.2
+  [ec485272] ArnoldiMethod v0.2.0
+  [7d9fca2a] Arpack v0.5.4
+  [4fba245c] ArrayInterface v7.4.11
+  [30b0a656] ArrayInterfaceCore v0.1.29
+  [a9b6321e] Atomix v0.1.0
+  [13072b0f] AxisAlgorithms v1.0.1
+  [ab4f0b2a] BFloat16s v0.4.2
+  [6e4b80f9] BenchmarkTools v1.3.2
+  [d1d4a3ce] BitFlags v0.1.7
+  [62783981] BitTwiddlingConvenienceFunctions v0.1.5
+  [fa961155] CEnum v0.4.2
+  [2a0fbf3d] CPUSummary v0.2.3
+  [052768ef] CUDA v4.4.0
+  [1af6417a] CUDA_Runtime_Discovery v0.2.2
+  [49dc2e85] Calculus v0.5.1
+  [082447d4] ChainRules v1.53.0
+  [d360d2e6] ChainRulesCore v1.16.0
+  [fb6a15b2] CloseOpenIntervals v0.1.12
+  [aaaa29a8] Clustering v0.15.4
+  [523fee87] CodecBzip2 v0.7.2
+  [944b1d66] CodecZlib v0.7.2
+  [35d6a980] ColorSchemes v3.22.0
+  [3da002f7] ColorTypes v0.11.4
+  [c3611d14] ColorVectorSpace v0.10.0
+  [5ae59095] Colors v0.12.10
+  [38540f10] CommonSolve v0.2.4
+  [bbf7d656] CommonSubexpressions v0.3.0
+  [34da2185] Compat v4.8.0
+  [b40a91a3] ComplementaritySolve v0.1.0 `..`
+  [2569d6c7] ConcreteStructs v0.2.3
+  [f0e56b4a] ConcurrentUtilities v2.2.1
+  [8f4d0f93] Conda v1.9.1
+  [187b0558] ConstructionBase v1.5.3
+  [d38c429a] Contour v0.6.2
+  [adafc99b] CpuId v0.3.1
+  [a8cc5b0e] Crayons v4.1.1
+  [9a962f9c] DataAPI v1.15.0
+  [124859b0] DataDeps v0.7.11
+  [a93c6f00] DataFrames v1.6.1
+  [864edb3b] DataStructures v0.18.14
+  [e2d170a0] DataValueInterfaces v1.0.0
+  [8bb1440f] DelimitedFiles v1.9.1
+  [2b5f629d] DiffEqBase v6.127.0
+  [163ba53b] DiffResults v1.1.0
+  [b552c78f] DiffRules v1.15.1
+  [b4f34e82] Distances v0.10.9
+  [31c24e10] Distributions v0.25.98
+  [ffbed154] DocStringExtensions v0.9.3
+  [fa6b7ba4] DualNumbers v0.6.8
+  [4e289a0a] EnumX v1.0.4
+  [460bff9d] ExceptionUnwrapping v0.1.9
+  [e2ba6199] ExprTools v0.1.10
+  [c87230d0] FFMPEG v0.4.1
+  [7a1cc6ca] FFTW v1.7.1
+  [7034ab61] FastBroadcast v0.2.6
+  [29a986be] FastLapackInterface v2.0.0
+  [1a297f60] FillArrays v1.5.0
+  [6a86dc24] FiniteDiff v2.21.1
+  [53c48c17] FixedPointNumbers v0.8.4
+  [59287772] Formatting v0.4.2
+  [f6369f11] ForwardDiff v0.10.35
+  [069b7b12] FunctionWrappers v1.1.3
+  [77dc65aa] FunctionWrappersWrappers v0.1.3
+  [0c68f7d7] GPUArrays v8.8.1
+  [46192b85] GPUArraysCore v0.1.5
+  [61eb1bfa] GPUCompiler v0.21.4
+  [28b8d3ca] GR v0.72.9
+⌃ [d7ba0133] Git v1.2.1
+  [86223c79] Graphs v1.8.0
+  [42e2da0e] Grisu v1.0.2
+  [cd3eb016] HTTP v1.9.14
+  [eafb193a] Highlights v0.5.2
+  [3e5b6fbb] HostCPUFeatures v0.1.15
+  [34004b35] HypergeometricFunctions v0.3.23
+  [7073ff75] IJulia v1.24.2
+  [7869d1d1] IRTools v0.4.10
+  [615f187c] IfElse v0.1.1
+  [d25df0c9] Inflate v0.1.3
+  [842dd82b] InlineStrings v1.4.0
+  [a98d9a8b] Interpolations v0.14.7
+  [41ab1584] InvertedIndices v1.3.0
+  [92d709cd] IrrationalConstants v0.2.2
+  [82899510] IteratorInterfaceExtensions v1.0.0
+  [1019f520] JLFzf v0.1.5
+  [692b3bcd] JLLWrappers v1.4.1
+  [682c06a0] JSON v0.21.4
+  [ef3ab10e] KLU v0.4.0
+  [63c18a36] KernelAbstractions v0.9.8
+  [5ab0869b] KernelDensity v0.6.7
+  [ba0b0d4f] Krylov v0.9.2
+  [929cbde3] LLVM v6.1.0
+  [b964fa9f] LaTeXStrings v1.3.0
+  [23fbe1c1] Latexify v0.16.1
+  [10f19ff3] LayoutPointers v0.1.14
+  [50d2b5c4] Lazy v0.15.1
+  [7ed4a6bd] LinearSolve v2.4.1
+  [2ab3a3ac] LogExpFunctions v0.3.24
+  [e6f89c97] LoggingExtras v1.0.0
+  [bdcacae8] LoopVectorization v0.12.165
+  [1914dd2f] MacroTools v0.5.10
+  [d125e4d3] ManualMemory v0.1.8
+  [b8f27783] MathOptInterface v1.18.0
+  [739be429] MbedTLS v1.1.7
+  [442fdcdd] Measures v0.3.2
+  [e1d29d7a] Missings v1.1.0
+  [46d2c3a1] MuladdMacro v0.2.4
+  [6f286f6a] MultivariateStats v0.10.2
+  [ffc61752] Mustache v1.0.17
+  [d8a4904e] MutableArithmetics v1.3.0
+  [872c559c] NNlib v0.9.4
+  [77ba4419] NaNMath v1.0.2
+  [b8a86587] NearestNeighbors v0.4.13
+  [8913a72c] NonlinearSolve v1.8.0
+  [510215fc] Observables v0.5.4
+  [6fe1bfb0] OffsetArrays v1.12.10
+  [4d8831e6] OpenSSL v1.4.1
+  [bac558e1] OrderedCollections v1.6.2
+  [f5f7c340] PATHSolver v1.4.2
+  [90014a1f] PDMats v0.11.17
+  [65ce6f38] PackageExtensionCompat v1.0.0
+  [d96e819e] Parameters v0.12.3
+  [69de0a69] Parsers v2.7.2
+  [b98c9c47] Pipe v1.3.0
+  [ccf2f8ad] PlotThemes v3.1.0
+  [995b91a9] PlotUtils v1.3.5
+  [91a5bcdd] Plots v1.38.17
+  [f517fe37] Polyester v0.7.5
+  [1d0040c9] PolyesterWeave v0.2.1
+  [2dfb63ee] PooledArrays v1.4.2
+  [d236fae5] PreallocationTools v0.4.12
+  [aea7be01] PrecompileTools v1.1.2
+  [21216c6a] Preferences v1.4.0
+  [08abe8d2] PrettyTables v2.2.7
+  [438e738f] PyCall v1.96.1
+  [d330b81b] PyPlot v2.11.1
+  [1fd47b50] QuadGK v2.8.2
+  [74087812] Random123 v1.6.1
+  [e6cf234a] RandomNumbers v1.5.3
+  [c84ed2f1] Ratios v0.4.5
+  [c1ae055f] RealDot v0.1.0
+  [3cdcf5f2] RecipesBase v1.3.4
+  [01d81517] RecipesPipeline v0.6.12
+  [731186ca] RecursiveArrayTools v2.38.7
+  [f2c3362d] RecursiveFactorization v0.2.18
+  [189a3867] Reexport v1.2.2
+  [05181044] RelocatableFolders v1.0.0
+  [ae029012] Requires v1.3.0
+  [79098fc4] Rmath v0.7.1
+  [7e49a35a] RuntimeGeneratedFunctions v0.5.11
+  [94e857df] SIMDTypes v0.1.0
+  [476501e8] SLEEFPirates v0.6.39
+  [0bca4576] SciMLBase v1.94.0
+  [31c91b34] SciMLBenchmarks v0.1.3
+  [c0aeaf25] SciMLOperators v0.3.5
+  [6c6a2e73] Scratch v1.2.0
+  [91c51154] SentinelArrays v1.4.0
+  [efcf1570] Setfield v1.1.1
+  [992d4aef] Showoff v1.0.3
+  [777ac1f9] SimpleBufferStream v1.1.0
+  [727e6d20] SimpleNonlinearSolve v0.1.18
+  [699a6c99] SimpleTraits v0.9.4
+  [66db9d55] SnoopPrecompile v1.0.3
+  [b85f4697] SoftGlobalScope v1.1.0
+  [a2af1166] SortingAlgorithms v1.1.1
+  [47a9eef4] SparseDiffTools v2.4.1
+  [e56a9233] Sparspak v0.3.9
+  [276daf66] SpecialFunctions v2.3.0
+  [860ef19b] StableRNGs v1.0.0
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+  [90137ffa] StaticArrays v1.6.2
+  [1e83bf80] StaticArraysCore v1.4.2
+  [82ae8749] StatsAPI v1.6.0
+  [2913bbd2] StatsBase v0.34.0
+  [4c63d2b9] StatsFuns v1.3.0
+  [f3b207a7] StatsPlots v0.15.6
+  [7792a7ef] StrideArraysCore v0.4.17
+  [69024149] StringEncodings v0.3.7
+  [892a3eda] StringManipulation v0.3.0
+  [09ab397b] StructArrays v0.6.15
+  [2efcf032] SymbolicIndexingInterface v0.2.2
+  [ab02a1b2] TableOperations v1.2.0
+  [3783bdb8] TableTraits v1.0.1
+  [bd369af6] Tables v1.10.1
+  [62fd8b95] TensorCore v0.1.1
+  [8290d209] ThreadingUtilities v0.5.2
+  [a759f4b9] TimerOutputs v0.5.23
+  [3bb67fe8] TranscodingStreams v0.9.13
+  [d5829a12] TriangularSolve v0.1.19
+  [410a4b4d] Tricks v0.1.7
+  [781d530d] TruncatedStacktraces v1.4.0
+  [5c2747f8] URIs v1.4.2
+  [3a884ed6] UnPack v1.0.2
+  [1cfade01] UnicodeFun v0.4.1
+  [1986cc42] Unitful v1.15.0
+  [45397f5d] UnitfulLatexify v1.6.3
+  [013be700] UnsafeAtomics v0.2.1
+  [d80eeb9a] UnsafeAtomicsLLVM v0.1.3
+  [41fe7b60] Unzip v0.2.0
+  [3d5dd08c] VectorizationBase v0.21.64
+  [81def892] VersionParsing v1.3.0
+  [19fa3120] VertexSafeGraphs v0.2.0
+  [44d3d7a6] Weave v0.10.12
+  [cc8bc4a8] Widgets v0.6.6
+  [efce3f68] WoodburyMatrices v0.5.5
+  [ddb6d928] YAML v0.4.9
+  [c2297ded] ZMQ v1.2.2
+  [e88e6eb3] Zygote v0.6.62
+  [700de1a5] ZygoteRules v0.2.3
+⌅ [68821587] Arpack_jll v3.5.1+1
+  [6e34b625] Bzip2_jll v1.0.8+0
+  [4ee394cb] CUDA_Driver_jll v0.5.0+1
+  [76a88914] CUDA_Runtime_jll v0.6.0+0
+  [83423d85] Cairo_jll v1.16.1+1
+  [2e619515] Expat_jll v2.5.0+0
+  [b22a6f82] FFMPEG_jll v4.4.2+2
+  [f5851436] FFTW_jll v3.3.10+0
+  [a3f928ae] Fontconfig_jll v2.13.93+0
+  [d7e528f0] FreeType2_jll v2.13.1+0
+  [559328eb] FriBidi_jll v1.0.10+0
+  [0656b61e] GLFW_jll v3.3.8+0
+  [d2c73de3] GR_jll v0.72.9+0
+  [78b55507] Gettext_jll v0.21.0+0
+⌅ [f8c6e375] Git_jll v2.34.1+0
+  [7746bdde] Glib_jll v2.74.0+2
+  [3b182d85] Graphite2_jll v1.3.14+0
+  [2e76f6c2] HarfBuzz_jll v2.8.1+1
+  [1d5cc7b8] IntelOpenMP_jll v2023.1.0+0
+  [aacddb02] JpegTurbo_jll v2.1.91+0
+  [c1c5ebd0] LAME_jll v3.100.1+0
+  [88015f11] LERC_jll v3.0.0+1
+  [dad2f222] LLVMExtra_jll v0.0.23+0
+  [1d63c593] LLVMOpenMP_jll v15.0.4+0
+  [dd4b983a] LZO_jll v2.10.1+0
+⌅ [e9f186c6] Libffi_jll v3.2.2+1
+  [d4300ac3] Libgcrypt_jll v1.8.7+0
+  [7e76a0d4] Libglvnd_jll v1.6.0+0
+  [7add5ba3] Libgpg_error_jll v1.42.0+0
+  [94ce4f54] Libiconv_jll v1.16.1+2
+  [4b2f31a3] Libmount_jll v2.35.0+0
+  [89763e89] Libtiff_jll v4.5.1+1
+  [38a345b3] Libuuid_jll v2.36.0+0
+  [856f044c] MKL_jll v2023.1.0+0
+  [e7412a2a] Ogg_jll v1.3.5+1
+⌅ [458c3c95] OpenSSL_jll v1.1.21+0
+  [efe28fd5] OpenSpecFun_jll v0.5.5+0
+  [91d4177d] Opus_jll v1.3.2+0
+  [30392449] Pixman_jll v0.42.2+0
+  [c0090381] Qt6Base_jll v6.4.2+3
+  [f50d1b31] Rmath_jll v0.4.0+0
+  [a2964d1f] Wayland_jll v1.21.0+0
+  [2381bf8a] Wayland_protocols_jll v1.25.0+0
+  [02c8fc9c] XML2_jll v2.10.3+0
+  [aed1982a] XSLT_jll v1.1.34+0
+  [ffd25f8a] XZ_jll v5.4.3+1
+  [4f6342f7] Xorg_libX11_jll v1.8.6+0
+  [0c0b7dd1] Xorg_libXau_jll v1.0.11+0
+  [935fb764] Xorg_libXcursor_jll v1.2.0+4
+  [a3789734] Xorg_libXdmcp_jll v1.1.4+0
+  [1082639a] Xorg_libXext_jll v1.3.4+4
+  [d091e8ba] Xorg_libXfixes_jll v5.0.3+4
+  [a51aa0fd] Xorg_libXi_jll v1.7.10+4
+  [d1454406] Xorg_libXinerama_jll v1.1.4+4
+  [ec84b674] Xorg_libXrandr_jll v1.5.2+4
+  [ea2f1a96] Xorg_libXrender_jll v0.9.10+4
+  [14d82f49] Xorg_libpthread_stubs_jll v0.1.1+0
+  [c7cfdc94] Xorg_libxcb_jll v1.15.0+0
+  [cc61e674] Xorg_libxkbfile_jll v1.1.2+0
+  [12413925] Xorg_xcb_util_image_jll v0.4.0+1
+  [2def613f] Xorg_xcb_util_jll v0.4.0+1
+  [975044d2] Xorg_xcb_util_keysyms_jll v0.4.0+1
+  [0d47668e] Xorg_xcb_util_renderutil_jll v0.3.9+1
+  [c22f9ab0] Xorg_xcb_util_wm_jll v0.4.1+1
+  [35661453] Xorg_xkbcomp_jll v1.4.6+0
+  [33bec58e] Xorg_xkeyboard_config_jll v2.39.0+0
+  [c5fb5394] Xorg_xtrans_jll v1.5.0+0
+  [8f1865be] ZeroMQ_jll v4.3.4+0
+  [3161d3a3] Zstd_jll v1.5.5+0
+⌅ [214eeab7] fzf_jll v0.29.0+0
+  [a4ae2306] libaom_jll v3.4.0+0
+  [0ac62f75] libass_jll v0.15.1+0
+  [f638f0a6] libfdk_aac_jll v2.0.2+0
+  [b53b4c65] libpng_jll v1.6.38+0
+  [a9144af2] libsodium_jll v1.0.20+0
+  [f27f6e37] libvorbis_jll v1.3.7+1
+  [1270edf5] x264_jll v2021.5.5+0
+  [dfaa095f] x265_jll v3.5.0+0
+  [d8fb68d0] xkbcommon_jll v1.4.1+0
+  [0dad84c5] ArgTools v1.1.1
+  [56f22d72] Artifacts
+  [2a0f44e3] Base64
+  [ade2ca70] Dates
+  [8ba89e20] Distributed
+  [f43a241f] Downloads v1.6.0
+  [7b1f6079] FileWatching
+  [9fa8497b] Future
+  [b77e0a4c] InteractiveUtils
+  [4af54fe1] LazyArtifacts
+  [b27032c2] LibCURL v0.6.4
+  [76f85450] LibGit2
+  [8f399da3] Libdl
+  [37e2e46d] LinearAlgebra
+  [56ddb016] Logging
+  [d6f4376e] Markdown
+  [a63ad114] Mmap
+  [ca575930] NetworkOptions v1.2.0
+  [44cfe95a] Pkg v1.10.0
+  [de0858da] Printf
+  [9abbd945] Profile
+  [3fa0cd96] REPL
+  [9a3f8284] Random
+  [ea8e919c] SHA v0.7.0
+  [9e88b42a] Serialization
+  [1a1011a3] SharedArrays
+  [6462fe0b] Sockets
+  [2f01184e] SparseArrays v1.10.0
+  [10745b16] Statistics v1.9.0
+  [4607b0f0] SuiteSparse
+  [fa267f1f] TOML v1.0.3
+  [a4e569a6] Tar v1.10.0
+  [8dfed614] Test
+  [cf7118a7] UUIDs
+  [4ec0a83e] Unicode
+  [e66e0078] CompilerSupportLibraries_jll v1.0.5+0
+  [deac9b47] LibCURL_jll v8.0.1+0
+  [29816b5a] LibSSH2_jll v1.10.2+0
+  [c8ffd9c3] MbedTLS_jll v2.28.2+0
+  [14a3606d] MozillaCACerts_jll v2023.1.10
+  [4536629a] OpenBLAS_jll v0.3.23+0
+  [05823500] OpenLibm_jll v0.8.1+0
+  [efcefdf7] PCRE2_jll v10.42.0+0
+  [bea87d4a] SuiteSparse_jll v7.2.0+0
+  [83775a58] Zlib_jll v1.2.13+0
+  [8e850b90] libblastrampoline_jll v5.8.0+0
+  [8e850ede] nghttp2_jll v1.52.0+0
+  [3f19e933] p7zip_jll v17.4.0+0
+Info Packages marked with ⌃ and ⌅ have new versions available, but those with ⌅ are restricted by compatibility constraints from upgrading. To see why use `status --outdated -m`
+```
+
diff --git a/benchmark/generated/script/lcp/solvers.jl b/benchmark/generated/script/lcp/solvers.jl
new file mode 100644
index 0000000..4ae4e3f
--- /dev/null
+++ b/benchmark/generated/script/lcp/solvers.jl
@@ -0,0 +1,245 @@
+
+import Pkg
+Pkg.activate(joinpath(@__DIR__, ".."))
+
+
+using CUDA, Statistics
+
+CUDA.allowscalar(false)
+
+iscuda(args...) = any(Base.Fix2(isa, CUDA.AnyCuArray), args)
+
+function timer(f, args...; numtimes::Int=10)
+    cuda_mode = iscuda(args...)
+    f(args...) # compile
+    times = zeros(numtimes)
+    for i in eachindex(times)
+        if cuda_mode
+            times[i] = @elapsed CUDA.@sync f(args...)
+        else
+            times[i] = @elapsed f(args...)
+        end
+    end
+    return minimum(times)
+end
+
+
+using BenchmarkTools, ComplementaritySolve, DataFrames, NonlinearSolve, PyPlot, StableRNGs
+
+
+A₁ = [2.0 1; 1 2.0]
+q₁ = [-5.0, 6.0]
+
+
+SOLVERS = [BokhovenIterativeAlgorithm(),
+    PGS(),
+    RPGS(),
+    InteriorPointMethod(),
+    NonlinearReformulation(),
+    NonlinearReformulation(:smooth, Broyden(; batched=true)),
+]
+times = zeros(length(SOLVERS), 2)
+solvers = ["Bok.", "PGS", "RPGS", "IPM", "NLR (Newton)", "NLR (Broyden)"]
+
+for (i, solver) in enumerate(SOLVERS)
+    @info "[CPU] UNBATCHED: Benchmarking $(solvers[i])"
+    prob_iip = LCP{true}(A₁, q₁, rand(StableRNG(0), 2))
+    prob_oop = LCP{false}(A₁, q₁, rand(StableRNG(0), 2))
+    times[i, 1] = timer(solve, prob_iip, solver)
+    times[i, 2] = timer(solve, prob_oop, solver)
+end
+
+
+let _=plt.xkcd()
+    xloc = 1:length(solvers)
+    width = 0.4  # the width of the bars
+    multiplier = 0
+    fig, ax = subplots(layout="constrained", figsize=(14, 6))
+    ax.set_yscale("log")
+
+    for (i, group) in enumerate(["Inplace", "Out of Place"])
+        offset = width * multiplier
+        rects = ax.bar(xloc .+ offset, times[:, i], width, label=group)
+        for (j, rect) in enumerate(rects)
+            height = rect.get_height()
+            ax.annotate("$(round(times[j, i] * 10^6; digits=2))μs",
+                        xy=(rect.get_x() + rect.get_width() / 2, height),
+                        xytext=(0, 3),  # 3 points vertical offset
+                        textcoords="offset points",
+                        ha="center", va="bottom")
+        end
+        multiplier += 1
+    end
+
+    ax.set_ylabel("Times (s)")
+    ax.set_title("[CPU] UNBATCHED: Basic LCP")
+    ax.set_xticks(xloc .+ width ./ 2, solvers)
+    ax.legend(ncols=3)
+    fig.tight_layout()
+    fig
+end
+
+
+SOLVERS = [BokhovenIterativeAlgorithm(Broyden(; batched=true)),
+    PGS(),
+    RPGS(),
+    InteriorPointMethod(),
+    NonlinearReformulation(:smooth, SimpleNewtonRaphson(; batched=true)),
+    NonlinearReformulation(:smooth, SimpleDFSane(; batched=true)),
+    NonlinearReformulation(:smooth, Broyden(; batched=true)),
+]
+BATCH_SIZES = 2 .^ (1:2:11)
+times = zeros(length(SOLVERS), length(BATCH_SIZES), 2)
+solvers = ["Bok.", "PGS", "RPGS", "IPM", "NLR (Newton)", "NLR (DFSane)", "NLR (Broyden)"]
+
+for (i, solver) in enumerate(SOLVERS)
+    @info "[CPU] BATCHED: Benchmarking $(solvers[i])"
+    for (j, N) in enumerate(BATCH_SIZES)
+        prob_iip = LCP{true}(A₁, q₁, rand(StableRNG(0), 2, N))
+        prob_oop = LCP{false}(A₁, q₁, rand(StableRNG(0), 2, N))
+        times[i, j, 2] = timer(solve, prob_oop, solver)
+        if i == 5
+            times[i, j, 1] = -1 # SimpleNewtonRaphson is not implemented for inplace
+            continue
+        end
+        times[i, j, 1] = timer(solve, prob_iip, solver)
+    end
+end
+
+
+let _=plt.xkcd()
+    prop_cycle = plt.rcParams["axes.prop_cycle"]
+    colors = prop_cycle.by_key()["color"]
+    fig, (ax1, ax2) = subplots(1, 2; layout="constrained", sharey=true, sharex=true, figsize=(16, 6))
+    ax1.set_yscale("log")
+    ax1.set_xscale("log")
+
+    fig.suptitle("[CPU] BATCHED: Basic LCP")
+    ax1.set_title("In-Place Solvers")
+    ax2.set_title("Out-Of-Place Solvers")
+
+    for (j, solver) in enumerate(solvers)
+        if !any(times[j, :, 1] .< 0)
+            ax1.plot(BATCH_SIZES, times[j, :, 1]; label=solver, color=colors[j])
+            ax1.scatter(BATCH_SIZES, times[j, :, 1]; color=colors[j])
+        end
+        if !any(times[j, :, 2] .< 0)
+            ax2.plot(BATCH_SIZES, times[j, :, 2]; label=solver, color=colors[j])
+            ax2.scatter(BATCH_SIZES, times[j, :, 2]; color=colors[j])
+        end
+    end
+
+    ax1.set_ylabel("Times (s)")
+    ax1.set_xlabel("Batch Size")
+    ax2.set_xlabel("Batch Size")
+    # ax1.legend(ncols=3)
+    ax2.legend(ncols=3)
+    fig.tight_layout()
+    fig
+end
+
+
+cuA₁ = [2.0 1; 1 2.0] |> cu
+cuq₁ = [-5.0, 6.0] |> cu
+
+
+SOLVERS = [BokhovenIterativeAlgorithm(Broyden(; batched=true)),
+    # InteriorPointMethod(),
+    NonlinearReformulation(:smooth, Broyden(; batched=true)),
+]
+times = zeros(length(SOLVERS), 2)
+solvers = ["Bok.", "NLR (Broyden)"]
+
+for (i, solver) in enumerate(SOLVERS)
+    @info "[CUDA] UNBATCHED: Benchmarking $(solvers[i])"
+    prob_iip = LCP{true}(cuA₁, cuq₁, rand(StableRNG(0), 2) |> cu)
+    prob_oop = LCP{false}(cuA₁, cuq₁, rand(StableRNG(0), 2) |> cu)
+    times[i, 1] = timer(solve, prob_iip, solver)
+    times[i, 2] = timer(solve, prob_oop, solver)
+end
+
+
+let _=plt.xkcd()
+    xloc = 1:length(solvers)
+    width = 0.4  # the width of the bars
+    multiplier = 0
+    fig, ax = subplots(layout="constrained", figsize=(14, 6))
+    ax.set_yscale("log")
+
+    for (i, group) in enumerate(["Inplace", "Out of Place"])
+        offset = width * multiplier
+        rects = ax.bar(xloc .+ offset, times[:, i], width, label=group)
+        for (j, rect) in enumerate(rects)
+            height = rect.get_height()
+            ax.annotate("$(round(times[j, i] * 10^6; digits=2))μs",
+                        xy=(rect.get_x() + rect.get_width() / 2, height),
+                        xytext=(0, 3),  # 3 points vertical offset
+                        textcoords="offset points",
+                        ha="center", va="bottom")
+        end
+        multiplier += 1
+    end
+
+    ax.set_ylabel("Times (s)")
+    ax.set_title("[CUDA] UNBATCHED: Basic LCP")
+    ax.set_xticks(xloc .+ width ./ 2, solvers)
+    ax.legend(ncols=3)
+    fig.tight_layout()
+    fig
+end
+
+
+SOLVERS = [BokhovenIterativeAlgorithm(Broyden(; batched=true)),
+    # InteriorPointMethod(),
+    NonlinearReformulation(:smooth, Broyden(; batched=true)),
+]
+BATCH_SIZES = 2 .^ (1:2:11)
+times = zeros(length(SOLVERS), length(BATCH_SIZES), 2)
+solvers = ["Bok.", "NLR (Broyden)"]
+
+for (i, solver) in enumerate(SOLVERS)
+    @info "[CUDA] BATCHED: Benchmarking $(solvers[i])"
+    for (j, N) in enumerate(BATCH_SIZES)
+        prob_iip = LCP{true}(cuA₁, cuq₁, rand(StableRNG(0), 2, N) |> cu)
+        prob_oop = LCP{false}(cuA₁, cuq₁, rand(StableRNG(0), 2, N) |> cu)
+        times[i, j, 2] = timer(solve, prob_oop, solver)
+        times[i, j, 1] = timer(solve, prob_iip, solver)
+    end
+end
+
+
+let _=plt.xkcd()
+    prop_cycle = plt.rcParams["axes.prop_cycle"]
+    colors = prop_cycle.by_key()["color"]
+    fig, (ax1, ax2) = subplots(1, 2; layout="constrained", sharey=true, sharex=true, figsize=(16, 6))
+    ax1.set_yscale("log")
+    ax1.set_xscale("log")
+
+    fig.suptitle("[CUDA] BATCHED: Basic LCP")
+    ax1.set_title("In-Place Solvers")
+    ax2.set_title("Out-Of-Place Solvers")
+
+    for (j, solver) in enumerate(solvers)
+        if !any(times[j, :, 1] .< 0)
+            ax1.plot(BATCH_SIZES, times[j, :, 1]; label=solver, color=colors[j])
+            ax1.scatter(BATCH_SIZES, times[j, :, 1]; color=colors[j])
+        end
+        if !any(times[j, :, 2] .< 0)
+            ax2.plot(BATCH_SIZES, times[j, :, 2]; label=solver, color=colors[j])
+            ax2.scatter(BATCH_SIZES, times[j, :, 2]; color=colors[j])
+        end
+    end
+
+    ax1.set_ylabel("Times (s)")
+    ax1.set_xlabel("Batch Size")
+    ax2.set_xlabel("Batch Size")
+    # ax1.legend(ncols=3)
+    ax2.legend(ncols=3)
+    fig.tight_layout()
+    fig
+end
+
+
+import SciMLBenchmarks
+SciMLBenchmarks.bench_footer(@__DIR__, last(splitdir(@__FILE__)))
+
diff --git a/benchmark/lcp/solvers.jmd b/benchmark/lcp/solvers.jmd
new file mode 100644
index 0000000..ea1280f
--- /dev/null
+++ b/benchmark/lcp/solvers.jmd
@@ -0,0 +1,283 @@
+# Benchmarking Available LCP Solvers
+
+```julia; echo = false
+import Pkg
+Pkg.activate(joinpath(@__DIR__, ".."))
+```
+
+## Useful Functions
+
+```julia
+using CUDA, Statistics
+
+CUDA.allowscalar(false)
+
+iscuda(args...) = any(Base.Fix2(isa, CUDA.AnyCuArray), args)
+
+function timer(f, args...; numtimes::Int=5)
+    cuda_mode = iscuda(args...)
+    f(args...) # compile
+    times = zeros(numtimes)
+    for i in eachindex(times)
+        if cuda_mode
+            times[i] = @elapsed CUDA.@sync f(args...)
+        else
+            times[i] = @elapsed f(args...)
+        end
+    end
+    return minimum(times)
+end
+```
+
+## Load Dependencies
+
+```julia
+using BenchmarkTools, ComplementaritySolve, DataFrames, NonlinearSolve, PyPlot, StableRNGs
+```
+
+## Basic LCP
+
+```julia
+A₁ = [2.0 1; 1 2.0]
+q₁ = [-5.0, 6.0]
+```
+
+### CPU Benchmarks
+
+#### Unbatched Version
+
+```julia
+SOLVERS = [BokhovenIterativeAlgorithm(),
+    PGS(),
+    RPGS(),
+    InteriorPointMethod(),
+    NonlinearReformulation(),
+    NonlinearReformulation(:smooth, Broyden(; batched=true)),
+]
+times = zeros(length(SOLVERS), 2)
+solvers = ["Bok.", "PGS", "RPGS", "IPM", "NLR (Newton)", "NLR (Broyden)"]
+
+for (i, solver) in enumerate(SOLVERS)
+    @info "[CPU] UNBATCHED: Benchmarking $(solvers[i])"
+    prob_iip = LCP{true}(A₁, q₁, rand(StableRNG(0), 2))
+    prob_oop = LCP{false}(A₁, q₁, rand(StableRNG(0), 2))
+    times[i, 1] = timer(solve, prob_iip, solver)
+    times[i, 2] = timer(solve, prob_oop, solver)
+end
+```
+
+```julia, echo = false
+let _=plt.xkcd()
+    xloc = 1:length(solvers)
+    width = 0.4  # the width of the bars
+    multiplier = 0
+    fig, ax = subplots(layout="constrained", figsize=(14, 6))
+    ax.set_yscale("log")
+
+    for (i, group) in enumerate(["Inplace", "Out of Place"])
+        offset = width * multiplier
+        rects = ax.bar(xloc .+ offset, times[:, i], width, label=group)
+        for (j, rect) in enumerate(rects)
+            height = rect.get_height()
+            ax.annotate("$(round(times[j, i] * 10^6; digits=2))μs",
+                        xy=(rect.get_x() + rect.get_width() / 2, height),
+                        xytext=(0, 3),  # 3 points vertical offset
+                        textcoords="offset points",
+                        ha="center", va="bottom")
+        end
+        multiplier += 1
+    end
+
+    ax.set_ylabel("Times (s)")
+    ax.set_title("[CPU] UNBATCHED: Basic LCP")
+    ax.set_xticks(xloc .+ width ./ 2, solvers)
+    ax.legend(ncols=3)
+    fig.tight_layout()
+    fig
+end
+```
+
+#### Batched Version
+
+Here we are batching the Problem with `N` starting values (typically batching LCPs involves
+batching multiple `M` and `q`)
+
+
+```julia
+SOLVERS = [BokhovenIterativeAlgorithm(Broyden(; batched=true)),
+    PGS(),
+    RPGS(),
+    InteriorPointMethod(),
+    NonlinearReformulation(:smooth, SimpleNewtonRaphson(; batched=true)),
+    NonlinearReformulation(:smooth, SimpleDFSane(; batched=true)),
+    NonlinearReformulation(:smooth, Broyden(; batched=true)),
+]
+BATCH_SIZES = 2 .^ (1:2:11)
+times = zeros(length(SOLVERS), length(BATCH_SIZES), 2)
+solvers = ["Bok.", "PGS", "RPGS", "IPM", "NLR (Newton)", "NLR (DFSane)", "NLR (Broyden)"]
+
+for (i, solver) in enumerate(SOLVERS)
+    @info "[CPU] BATCHED: Benchmarking $(solvers[i])"
+    for (j, N) in enumerate(BATCH_SIZES)
+        prob_iip = LCP{true}(A₁, q₁, rand(StableRNG(0), 2, N))
+        prob_oop = LCP{false}(A₁, q₁, rand(StableRNG(0), 2, N))
+        times[i, j, 2] = timer(solve, prob_oop, solver)
+        if i == 5
+            times[i, j, 1] = -1 # SimpleNewtonRaphson is not implemented for inplace
+            continue
+        end
+        times[i, j, 1] = timer(solve, prob_iip, solver)
+    end
+end
+```
+
+```julia, echo = false
+let _=plt.xkcd()
+    prop_cycle = plt.rcParams["axes.prop_cycle"]
+    colors = prop_cycle.by_key()["color"]
+    fig, (ax1, ax2) = subplots(1, 2; layout="constrained", sharey=true, sharex=true, figsize=(16, 6))
+    ax1.set_yscale("log")
+    ax1.set_xscale("log")
+
+    fig.suptitle("[CPU] BATCHED: Basic LCP")
+    ax1.set_title("In-Place Solvers")
+    ax2.set_title("Out-Of-Place Solvers")
+
+    for (j, solver) in enumerate(solvers)
+        if !any(times[j, :, 1] .< 0)
+            ax1.plot(BATCH_SIZES, times[j, :, 1]; label=solver, color=colors[j])
+            ax1.scatter(BATCH_SIZES, times[j, :, 1]; color=colors[j])
+        end
+        if !any(times[j, :, 2] .< 0)
+            ax2.plot(BATCH_SIZES, times[j, :, 2]; label=solver, color=colors[j])
+            ax2.scatter(BATCH_SIZES, times[j, :, 2]; color=colors[j])
+        end
+    end
+
+    ax1.set_ylabel("Times (s)")
+    ax1.set_xlabel("Batch Size")
+    ax2.set_xlabel("Batch Size")
+    # ax1.legend(ncols=3)
+    ax2.legend(ncols=3)
+    fig.tight_layout()
+    fig
+end
+```
+
+### CUDA Benchmarks
+
+```julia
+cuA₁ = [2.0 1; 1 2.0] |> cu
+cuq₁ = [-5.0, 6.0] |> cu
+```
+
+#### Unbatched Version
+
+```julia
+SOLVERS = [BokhovenIterativeAlgorithm(Broyden(; batched=true)),
+    # InteriorPointMethod(),
+    NonlinearReformulation(:smooth, Broyden(; batched=true)),
+]
+times = zeros(length(SOLVERS), 2)
+solvers = ["Bok.", "NLR (Broyden)"]
+
+for (i, solver) in enumerate(SOLVERS)
+    @info "[CUDA] UNBATCHED: Benchmarking $(solvers[i])"
+    prob_iip = LCP{true}(cuA₁, cuq₁, rand(StableRNG(0), 2) |> cu)
+    prob_oop = LCP{false}(cuA₁, cuq₁, rand(StableRNG(0), 2) |> cu)
+    times[i, 1] = timer(solve, prob_iip, solver)
+    times[i, 2] = timer(solve, prob_oop, solver)
+end
+```
+
+```julia, echo = false
+let _=plt.xkcd()
+    xloc = 1:length(solvers)
+    width = 0.4  # the width of the bars
+    multiplier = 0
+    fig, ax = subplots(layout="constrained", figsize=(14, 6))
+    ax.set_yscale("log")
+
+    for (i, group) in enumerate(["Inplace", "Out of Place"])
+        offset = width * multiplier
+        rects = ax.bar(xloc .+ offset, times[:, i], width, label=group)
+        for (j, rect) in enumerate(rects)
+            height = rect.get_height()
+            ax.annotate("$(round(times[j, i] * 10^6; digits=2))μs",
+                        xy=(rect.get_x() + rect.get_width() / 2, height),
+                        xytext=(0, 3),  # 3 points vertical offset
+                        textcoords="offset points",
+                        ha="center", va="bottom")
+        end
+        multiplier += 1
+    end
+
+    ax.set_ylabel("Times (s)")
+    ax.set_title("[CUDA] UNBATCHED: Basic LCP")
+    ax.set_xticks(xloc .+ width ./ 2, solvers)
+    ax.legend(ncols=3)
+    fig.tight_layout()
+    fig
+end
+```
+
+#### Batched Version
+
+
+```julia
+SOLVERS = [BokhovenIterativeAlgorithm(Broyden(; batched=true)),
+    # InteriorPointMethod(),
+    NonlinearReformulation(:smooth, Broyden(; batched=true)),
+]
+BATCH_SIZES = 2 .^ (1:2:11)
+times = zeros(length(SOLVERS), length(BATCH_SIZES), 2)
+solvers = ["Bok.", "NLR (Broyden)"]
+
+for (i, solver) in enumerate(SOLVERS)
+    @info "[CUDA] BATCHED: Benchmarking $(solvers[i])"
+    for (j, N) in enumerate(BATCH_SIZES)
+        prob_iip = LCP{true}(cuA₁, cuq₁, rand(StableRNG(0), 2, N) |> cu)
+        prob_oop = LCP{false}(cuA₁, cuq₁, rand(StableRNG(0), 2, N) |> cu)
+        times[i, j, 2] = timer(solve, prob_oop, solver)
+        times[i, j, 1] = timer(solve, prob_iip, solver)
+    end
+end
+```
+
+```julia, echo = false
+let _=plt.xkcd()
+    prop_cycle = plt.rcParams["axes.prop_cycle"]
+    colors = prop_cycle.by_key()["color"]
+    fig, (ax1, ax2) = subplots(1, 2; layout="constrained", sharey=true, sharex=true, figsize=(16, 6))
+    ax1.set_yscale("log")
+    ax1.set_xscale("log")
+
+    fig.suptitle("[CUDA] BATCHED: Basic LCP")
+    ax1.set_title("In-Place Solvers")
+    ax2.set_title("Out-Of-Place Solvers")
+
+    for (j, solver) in enumerate(solvers)
+        if !any(times[j, :, 1] .< 0)
+            ax1.plot(BATCH_SIZES, times[j, :, 1]; label=solver, color=colors[j])
+            ax1.scatter(BATCH_SIZES, times[j, :, 1]; color=colors[j])
+        end
+        if !any(times[j, :, 2] .< 0)
+            ax2.plot(BATCH_SIZES, times[j, :, 2]; label=solver, color=colors[j])
+            ax2.scatter(BATCH_SIZES, times[j, :, 2]; color=colors[j])
+        end
+    end
+
+    ax1.set_ylabel("Times (s)")
+    ax1.set_xlabel("Batch Size")
+    ax2.set_xlabel("Batch Size")
+    # ax1.legend(ncols=3)
+    ax2.legend(ncols=3)
+    fig.tight_layout()
+    fig
+end
+```
+
+```julia, echo = false
+import SciMLBenchmarks
+SciMLBenchmarks.bench_footer(@__DIR__, last(splitdir(@__FILE__)))
+```
diff --git a/src/ComplementaritySolve.jl b/src/ComplementaritySolve.jl
index cfc6162..00c3bbb 100644
--- a/src/ComplementaritySolve.jl
+++ b/src/ComplementaritySolve.jl
@@ -33,6 +33,25 @@ const AA3 = AbstractArray{T, 3} where {T}
 ### ----- Type Piracy Starts ----- ###
 ArrayInterfaceCore.can_setindex(::Type{<:AbstractFill}) = false
 ArrayInterfaceCore.can_setindex(::Zygote.OneElement) = false
+
+import LinearSolve: DefaultLinearSolver, DefaultAlgorithmChoice
+
+function LinearSolve.defaultalg(A::SciMLBase.AbstractSciMLOperator,
+    b::LinearSolve.GPUArraysCore.AbstractGPUArray,
+    assump::LinearSolve.OperatorAssumptions)
+    if has_ldiv!(A)
+        return DefaultLinearSolver(DefaultAlgorithmChoice.DirectLdiv!)
+    elseif !assump.issq
+        m, n = size(A)
+        if m < n
+            DefaultLinearSolver(DefaultAlgorithmChoice.KrylovJL_CRAIGMR)
+        else
+            DefaultLinearSolver(DefaultAlgorithmChoice.KrylovJL_LSMR)
+        end
+    else
+        DefaultLinearSolver(DefaultAlgorithmChoice.KrylovJL_GMRES)
+    end
+end
 ### ------ Type Piracy Ends ------ ###
 
 abstract type AbstractComplementarityAlgorithm end
diff --git a/src/algorithms/lcp/bokhoven_iterative.jl b/src/algorithms/lcp/bokhoven_iterative.jl
index 37660a9..8255f82 100644
--- a/src/algorithms/lcp/bokhoven_iterative.jl
+++ b/src/algorithms/lcp/bokhoven_iterative.jl
@@ -7,38 +7,39 @@ BokhovenIterativeAlgorithm() = BokhovenIterativeAlgorithm(NewtonRaphson())
 
 @truncate_stacktrace BokhovenIterativeAlgorithm
 
-## NOTE: It is a steady state problem so we could in-principle use an ODE Solver
-function __solve(prob::LinearComplementarityProblem{iip, false},
-    alg::BokhovenIterativeAlgorithm,
-    u0,
-    M,
-    q;
-    kwargs...) where {iip}
-    A = pinv(I + M)
-    B = A * (I - M)
-    b = -A * q
-
-    θ = vcat(vec(B), b)
-
-    _get_B(θ) = reshape(view(θ, 1:length(B)), size(B))
-    _get_b(θ) = view(θ, (length(B) + 1):length(θ))
-
-    if iip
-        function objective!(residual, u, θ)
-            mul!(residual, _get_B(θ), abs.(u))
-            residual .+= _get_b(θ) .- u
-            return residual
+for batched in (true, false)
+    @eval @views function __solve(prob::LinearComplementarityProblem{iip, $batched},
+        alg::BokhovenIterativeAlgorithm,
+        u0,
+        M,
+        q;
+        kwargs...) where {iip}
+        A = I➕x⁻¹(M)
+        B = matmul(A, I➖x(M))
+        b = -matmul(A, q)
+
+        θ = vcat(vec(B), b)
+
+        _get_B(θ) = reshape(view(θ, 1:length(B)), size(B))
+        _get_b(θ) = reshape(view(θ, (length(B) + 1):length(θ)), size(b))
+
+        if iip
+            function objective!(residual, u, θ)
+                residual .= _get_b(θ) .- u
+                matmul!(residual, _get_B(θ), abs.(u), true, true)
+                return residual
+            end
+
+            _prob = NonlinearProblem(NonlinearFunction{true}(objective!), u0, θ)
+        else
+            objective(u, θ) = matmul(_get_B(θ), abs.(u)) .+ _get_b(θ) .- u
+
+            _prob = NonlinearProblem(NonlinearFunction{false}(objective), u0, θ)
         end
+        sol = solve(_prob, alg.nlsolver; kwargs...)
 
-        _prob = NonlinearProblem(NonlinearFunction{true}(objective!), u0, θ)
-    else
-        objective(u, θ) = _get_B(θ) * abs.(u) .+ _get_b(θ) .- u
+        z = abs.(sol.u) .+ sol.u
 
-        _prob = NonlinearProblem(NonlinearFunction{false}(objective), u0, θ)
+        return LinearComplementaritySolution(z, sol.resid, prob, alg, sol.retcode)
     end
-    sol = solve(_prob, alg.nlsolver; kwargs...)
-
-    z = abs.(sol.u) .+ sol.u
-
-    return LinearComplementaritySolution(z, sol.resid, prob, alg, sol.retcode)
 end
diff --git a/src/algorithms/lcp/fallback.jl b/src/algorithms/lcp/fallback.jl
index 67e20d7..af4490e 100644
--- a/src/algorithms/lcp/fallback.jl
+++ b/src/algorithms/lcp/fallback.jl
@@ -1,4 +1,5 @@
-@views function __solve(prob::LinearComplementarityProblem{iip, true},
+# Can't use views here because it fails for some downstream solvers
+function __solve(prob::LinearComplementarityProblem{iip, true},
     solver::AbstractComplementarityAlgorithm,
     u0,
     M,
diff --git a/src/algorithms/lcp/ipm.jl b/src/algorithms/lcp/ipm.jl
index e48343e..cd717d7 100644
--- a/src/algorithms/lcp/ipm.jl
+++ b/src/algorithms/lcp/ipm.jl
@@ -24,7 +24,8 @@ function __make_ipm_linsolve_operator(M, zₖ, wₖ, Δzw, ::Val{batched}) where
             u = reshape(u, 2L, :)
         end
         Δz, Δw = selectdim(u, 1, 1:L), selectdim(u, 1, (L + 1):(2L))
-        selectdim(v, 1, 1:L) .= matmul(M, Δz) .- Δw
+        selectdim(v, 1, 1:L) .= Δw
+        matmul!(selectdim(v, 1, 1:L), M, Δz, true, -1)
         selectdim(v, 1, (L + 1):(2L)) .= zₖ .* Δw .+ wₖ .* Δz
         return vec(v)
     end
diff --git a/src/utils.jl b/src/utils.jl
index 95d1d04..d67a6d5 100644
--- a/src/utils.jl
+++ b/src/utils.jl
@@ -46,7 +46,7 @@ end
     y_ = reshape(y, size(y, 1), 1, size(y, 2))
     x_ = reshape(x, size(x, 1), 1, size(x, 2))
     batched_mul!(y_, A, x_, α, β)
-    return y_[:, 1, :]
+    return dropdims(y_; dims=2)
 end
 
 ## Matmul with proper dispatches
@@ -93,3 +93,22 @@ function __check_correct_batching(args::Int...)
     end
     return batch_size
 end
+
+# Pseudo Inverse
+I➕x⁻¹(x::AbstractMatrix) = pinv(I + x)
+@views function I➕x⁻¹(x::AbstractArray{T, 3}) where {T}
+    y = similar(x)
+    for i in 1:size(x, 3)
+        y[:, :, i] .= pinv(I + x[:, :, i])
+    end
+    return y
+end
+
+I➖x(x::AbstractMatrix) = I - x
+@views function I➖x(x::AbstractArray{T, 3}) where {T}
+    y = similar(x)
+    for i in 1:size(x, 3)
+        y[:, :, i] .= I - x[:, :, i]
+    end
+    return y
+end