Optimization.jl: A Unified Optimization Package

Optimization.jl provides the easiest way to create an optimization problem and solve it. It enables rapid prototyping and experimentation with minimal syntax overhead by providing a uniform interface to >25 optimization libraries, hence 100+ optimization solvers encompassing almost all classes of optimization algorithms such as global, mixed-integer, non-convex, second-order local, constrained, etc. It allows you to choose an Automatic Differentiation (AD) backend by simply passing an argument to indicate the package to use and automatically generates the efficient derivatives of the objective and constraints while giving you the flexibility to switch between different AD engines as per your problem. Additionally, Optimization.jl takes care of passing problem specific information to solvers that can leverage it such as the sparsity pattern of the hessian or constraint jacobian and the expression graph.

It extends the common SciML interface making it very easy to use for anyone familiar with the SciML ecosystem. It is also very easy to extend to new solvers and new problem types. The package is actively maintained and new features are added regularly.

Installation

In most instances you'll want to use some solver directly. For example, to use the Optim set of solvers, you'd do:

Pkg.add("OptimizationOptimJL")

See the solver lists for more details. In many scenarios it's recommended to have some automatic differentiation (AD) package installed, most tutorials will use some form AD and thus require installing the associated AD package. AD choices are made with ADTypes, and thus it's recommended you also add the ADTypes.jl package for most use cases.

Optimization.jl is simply a bundle/interface over many of these dependencies. It may add some optional higher level behavior in the future but at this time the top level package does not add any extra behavior.

Contributing

Overview of the solver packages in alphabetical order

BlackBoxOptim - Global Methods - Zeroth order - Unconstrained - Box Constraints
CMAEvolutionaryStrategy - Global Methods - Zeroth order - Unconstrained - Box Constraints
Evolutionary - Global Methods - Zeroth order - Unconstrained - Box Constraints - Non-linear Constraints
GCMAES - Global Methods - First order - Box Constraints - Unconstrained
Manopt - Local Methods - First order - Second order - Zeroth order - Box Constraints - Constrained 🟡 - Global Methods - Zeroth order - Unconstrained
MathOptInterface - Local Methods - First order - Second order - Box Constraints - Constrained - Global Methods - First order - Second order - Constrained
MultistartOptimization - Global Methods - Zeroth order - First order - Second order - Box Constraints
Metaheuristics - Global Methods - Zeroth order - Unconstrained - Box Constraints
NOMAD - Global Methods - Zeroth order - Unconstrained - Box Constraints - Constrained 🟡
NLopt - Local Methods - First order - Zeroth order - Second order 🟡 - Box Constraints - Local Constrained 🟡 - Global Methods - Zeroth order - First order - Unconstrained - Constrained 🟡
Optim - Local Methods - Zeroth order - First order - Second order - Box Constraints - Constrained - Global Methods - Zeroth order - Unconstrained - Box Constraints
PRIMA - Local Methods - Derivative-Free: ✅ - **Constraints** - Box Constraints: ✅ - Local Constrained: ✅
QuadDIRECT - **Constraints** - Box Constraints: ✅ - Global Methods - Unconstrained: ✅

🟡 = supported in downstream library but not yet implemented in Optimization.jl; PR to add this functionality are welcome

Citation

@software{vaibhav_kumar_dixit_2023_7738525,
	author = {Vaibhav Kumar Dixit and Christopher Rackauckas},
	month = mar,
	publisher = {Zenodo},
	title = {Optimization.jl: A Unified Optimization Package},
	version = {v3.12.1},
	doi = {10.5281/zenodo.7738525},
  	url = {https://doi.org/10.5281/zenodo.7738525},
	year = 2023}

Reproducibility

The documentation of this SciML package was built using these direct dependencies,
Status `~/work/Optimization.jl/Optimization.jl/docs/Project.toml`
  [47edcb42] ADTypes v1.22.1
  [7c4d4715] AmplNLWriter v1.4.1
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  [a0c0ee7d] DifferentiationInterface v0.7.18
  [e30172f5] Documenter v1.17.0
  [6a86dc24] FiniteDiff v2.31.1
  [f6369f11] ForwardDiff v1.4.1
  [87dc4568] HiGHS v1.24.0
  [b6b21f68] Ipopt v1.15.0
  [c8e1da08] IterTools v1.10.0
  [2ddba703] Juniper v0.9.4
  [b2108857] Lux v1.31.4
  [f1d291b0] MLUtils v0.4.12
  [1cead3c2] Manifolds v0.11.28
 [0fc0a36d] Manopt v0.5.39
  [961ee093] ModelingToolkit v11.31.0
  [a4795742] NLPModels v0.21.12
  [7998695d] NLPModelsTest v0.10.9
  [76087f3c] NLopt v1.2.1
  [7f7a1694] Optimization v5.6.2 `~/work/Optimization.jl/Optimization.jl`
  [2ea93f80] OptimizationAuglag v2.0.1 `../lib/OptimizationAuglag`
  [3e6eede4] OptimizationBBO v0.4.8 `../lib/OptimizationBBO`
  [bca83a33] OptimizationBase v5.1.4 `../lib/OptimizationBase`
  [bd407f91] OptimizationCMAEvolutionStrategy v0.3.9 `../lib/OptimizationCMAEvolutionStrategy`
  [cb963754] OptimizationEvolutionary v0.4.10 `../lib/OptimizationEvolutionary`
  [6f0a0517] OptimizationGCMAES v0.3.9 `../lib/OptimizationGCMAES`
  [43fad042] OptimizationIpopt v1.2.2 `../lib/OptimizationIpopt`
  [22f7324a] OptimizationLBFGSB v1.4.2 `../lib/OptimizationLBFGSB`
  [fd9f6733] OptimizationMOI v1.3.2 `../lib/OptimizationMOI`
  [5d9c809f] OptimizationMadNLP v2.2.1 `../lib/OptimizationMadNLP`
  [e57b7fff] OptimizationManopt v1.3.3 `../lib/OptimizationManopt`
  [3aafef2f] OptimizationMetaheuristics v0.3.7 `../lib/OptimizationMetaheuristics`
  [e4316d97] OptimizationMultistartOptimization v0.3.6 `../lib/OptimizationMultistartOptimization`
  [064b21be] OptimizationNLPModels v1.3.2 `../lib/OptimizationNLPModels`
  [4e6fcdb7] OptimizationNLopt v0.3.12 `../lib/OptimizationNLopt`
  [2cab0595] OptimizationNOMAD v0.3.7 `../lib/OptimizationNOMAD`
  [dfa73e59] OptimizationODE v0.1.7 `../lib/OptimizationODE`
  [36348300] OptimizationOptimJL v0.4.15 `../lib/OptimizationOptimJL`
  [42dfb2eb] OptimizationOptimisers v0.3.18 `../lib/OptimizationOptimisers`
  [72f8369c] OptimizationPRIMA v0.3.9 `../lib/OptimizationPRIMA`
  [500b13db] OptimizationPolyalgorithms v0.3.7 `../lib/OptimizationPolyalgorithms`
  [fb0822aa] OptimizationPyCMA v1.3.2 `../lib/OptimizationPyCMA`
  [842ac81e] OptimizationQuadDIRECT v0.3.6 `../lib/OptimizationQuadDIRECT`
  [cce07bd8] OptimizationSciPy v0.4.7 `../lib/OptimizationSciPy`
  [892fee11] OptimizationSophia v1.3.2 `../lib/OptimizationSophia`
  [3d669222] OptimizationSpeedMapping v0.2.6 `../lib/OptimizationSpeedMapping`
  [1dea7af3] OrdinaryDiffEq v7.1.1
  [91a5bcdd] Plots v1.41.6
  [dae52e8d] QuadDIRECT v0.1.2 `https://github.com/timholy/QuadDIRECT.jl.git#`
  [37e2e3b7] ReverseDiff v1.17.0
  [0bca4576] SciMLBase v3.31.0
  [1ed8b502] SciMLSensitivity v7.113.0
  [510db2f7] SimpleOptimization v1.2.2 `../lib/SimpleOptimization`
  [0c5d862f] Symbolics v7.30.0
  [9f7883ad] Tracker v0.2.38
  [e88e6eb3] Zygote v0.7.11
  [9cc047cb] Ipopt_jll v300.1400.1902+0
  [9a3f8284] Random v1.11.0
Info Packages marked with  have new versions available but compatibility constraints restrict them from upgrading. To see why use `status --outdated`
and using this machine and Julia version.
Julia Version 1.12.6
Commit 15346901f00 (2026-04-09 19:20 UTC)
Build Info:
  Official https://julialang.org release
Platform Info:
  OS: Linux (x86_64-linux-gnu)
  CPU: 4 × AMD EPYC 7763 64-Core Processor
  WORD_SIZE: 64
  LLVM: libLLVM-18.1.7 (ORCJIT, znver3)
  GC: Built with stock GC
Threads: 1 default, 1 interactive, 1 GC (on 4 virtual cores)
A more complete overview of all dependencies and their versions is also provided.
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  [d1185830] SymbolicUtils v4.38.1
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 [c3b1956e] TypeUtils v1.14.0
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  [1d5cc7b8] IntelOpenMP_jll v2025.2.0+0
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  [c1c5ebd0] LAME_jll v3.100.3+0
  [88015f11] LERC_jll v4.1.0+0
  [dad2f222] LLVMExtra_jll v0.0.43+1
  [1d63c593] LLVMOpenMP_jll v21.1.8+0
  [81d17ec3] L_BFGS_B_jll v3.0.1+0
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 [e9f186c6] Libffi_jll v3.4.7+0
  [7e76a0d4] Libglvnd_jll v1.7.1+1
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  [4b2f31a3] Libmount_jll v2.42.0+0
  [89763e89] Libtiff_jll v4.7.3+0
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  [d7ed1dd3] MUMPS_seq_jll v500.900.0+0
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 [2fc7fd02] NOMAD_jll v4.3.1+0
  [e7412a2a] Ogg_jll v1.3.6+0
  [656ef2d0] OpenBLAS32_jll v0.3.33+2
  [9bd350c2] OpenSSH_jll v10.4.1+0
  [efe28fd5] OpenSpecFun_jll v0.5.6+0
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  [eead6e0c] PRIMA_jll v0.7.1+0
  [36c8627f] Pango_jll v1.57.1+0
  [30392449] Pixman_jll v0.46.4+0
  [c0090381] Qt6Base_jll v6.10.2+2
  [629bc702] Qt6Declarative_jll v6.10.2+2
  [ce943373] Qt6ShaderTools_jll v6.10.2+1
  [6de9746b] Qt6Svg_jll v6.10.2+0
  [e99dba38] Qt6Wayland_jll v6.10.2+1
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  [319450e9] SPRAL_jll v2025.9.18+0
  [a44049a8] Vulkan_Loader_jll v1.3.243+0
  [a2964d1f] Wayland_jll v1.24.0+0
 [02c8fc9c] XML2_jll v2.13.9+0
  [ffd25f8a] XZ_jll v5.8.3+0
  [f67eecfb] Xorg_libICE_jll v1.1.2+0
  [c834827a] Xorg_libSM_jll v1.2.6+0
  [4f6342f7] Xorg_libX11_jll v1.8.13+0
  [0c0b7dd1] Xorg_libXau_jll v1.0.13+0
  [935fb764] Xorg_libXcursor_jll v1.2.4+0
  [a3789734] Xorg_libXdmcp_jll v1.1.6+0
  [1082639a] Xorg_libXext_jll v1.3.8+0
  [d091e8ba] Xorg_libXfixes_jll v6.0.2+0
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  [d1454406] Xorg_libXinerama_jll v1.1.7+0
  [ec84b674] Xorg_libXrandr_jll v1.5.6+0
  [ea2f1a96] Xorg_libXrender_jll v0.9.12+0
  [a65dc6b1] Xorg_libpciaccess_jll v0.19.0+0
  [c7cfdc94] Xorg_libxcb_jll v1.17.1+0
  [cc61e674] Xorg_libxkbfile_jll v1.2.0+0
  [e920d4aa] Xorg_xcb_util_cursor_jll v0.1.6+0
  [12413925] Xorg_xcb_util_image_jll v0.4.1+0
  [2def613f] Xorg_xcb_util_jll v0.4.1+0
  [975044d2] Xorg_xcb_util_keysyms_jll v0.4.1+0
  [0d47668e] Xorg_xcb_util_renderutil_jll v0.3.10+0
  [c22f9ab0] Xorg_xcb_util_wm_jll v0.4.2+0
  [35661453] Xorg_xkbcomp_jll v1.4.7+0
  [33bec58e] Xorg_xkeyboard_config_jll v2.47.0+1
  [c5fb5394] Xorg_xtrans_jll v1.6.0+0
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  [a4ae2306] libaom_jll v3.13.3+0
  [0ac62f75] libass_jll v0.17.4+0
  [1183f4f0] libdecor_jll v0.2.2+0
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  [2db6ffa8] libevdev_jll v1.13.4+0
  [f638f0a6] libfdk_aac_jll v2.0.4+0
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 [1270edf5] x264_jll v10164.0.1+0
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  [0dad84c5] ArgTools v1.1.2
  [56f22d72] Artifacts v1.11.0
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  [ade2ca70] Dates v1.11.0
  [8ba89e20] Distributed v1.11.0
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  [7b1f6079] FileWatching v1.11.0
  [9fa8497b] Future v1.11.0
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  [ac6e5ff7] JuliaSyntaxHighlighting v1.12.0
  [4af54fe1] LazyArtifacts v1.11.0
  [b27032c2] LibCURL v0.6.4
  [76f85450] LibGit2 v1.11.0
  [8f399da3] Libdl v1.11.0
  [37e2e46d] LinearAlgebra v1.12.0
  [56ddb016] Logging v1.11.0
  [d6f4376e] Markdown v1.11.0
  [a63ad114] Mmap v1.11.0
  [ca575930] NetworkOptions v1.3.0
  [44cfe95a] Pkg v1.12.1
  [de0858da] Printf v1.11.0
  [3fa0cd96] REPL v1.11.0
  [9a3f8284] Random v1.11.0
  [ea8e919c] SHA v0.7.0
  [9e88b42a] Serialization v1.11.0
  [6462fe0b] Sockets v1.11.0
  [2f01184e] SparseArrays v1.12.0
  [f489334b] StyledStrings v1.11.0
  [4607b0f0] SuiteSparse
  [fa267f1f] TOML v1.0.3
  [a4e569a6] Tar v1.10.0
  [8dfed614] Test v1.11.0
  [cf7118a7] UUIDs v1.11.0
  [4ec0a83e] Unicode v1.11.0
  [e66e0078] CompilerSupportLibraries_jll v1.3.0+1
  [deac9b47] LibCURL_jll v8.15.0+0
  [e37daf67] LibGit2_jll v1.9.0+0
  [29816b5a] LibSSH2_jll v1.11.3+1
  [14a3606d] MozillaCACerts_jll v2025.11.4
  [4536629a] OpenBLAS_jll v0.3.29+0
  [05823500] OpenLibm_jll v0.8.7+0
  [458c3c95] OpenSSL_jll v3.5.4+0
  [efcefdf7] PCRE2_jll v10.44.0+1
  [bea87d4a] SuiteSparse_jll v7.8.3+2
  [83775a58] Zlib_jll v1.3.1+2
  [8e850b90] libblastrampoline_jll v5.15.0+0
  [8e850ede] nghttp2_jll v1.64.0+1
  [3f19e933] p7zip_jll v17.7.0+0
Info Packages marked with  have new versions available but compatibility constraints restrict them from upgrading. To see why use `status --outdated -m`

You can also download the manifest file and the project file.