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
Assuming that you already have Julia correctly installed, it suffices to import Optimization.jl in the standard way:
import Pkg
Pkg.add("Optimization")The packages relevant to the core functionality of Optimization.jl will be imported accordingly and, in most cases, you do not have to worry about the manual installation of dependencies. Optimization.jl natively offers a LBFGS solver but for more solver choices (discussed below in Optimization Packages), you will need to add the specific wrapper packages.
Contributing
Please refer to the SciML ColPrac: Contributor's Guide on Collaborative Practices for Community Packages for guidance on PRs, issues, and other matters relating to contributing to SciML.
See the SciML Style Guide for common coding practices and other style decisions.
There are a few community forums:
- The #diffeq-bridged and #sciml-bridged channels in the Julia Slack
- The #diffeq-bridged and #sciml-bridged channels in the Julia Zulip
- On the Julia Discourse forums
- See also SciML Community page
Overview of the solver packages in alphabetical order
<details> <summary><strong>BlackBoxOptim</strong></summary>
- Global Methods
- Zeroth order
- Unconstrained
- Box Constraints
</details> <details> <summary><strong>CMAEvolutionaryStrategy</strong></summary>
- Global Methods
- Zeroth order
- Unconstrained
- Box Constraints
</details> <details> <summary><strong>Evolutionary</strong></summary>
- Global Methods
- Zeroth order
- Unconstrained
- Box Constraints
- Non-linear Constraints
</details> <details> <summary><strong>GCMAES</strong></summary>
- Global Methods
- First order
- Box Constraints
- Unconstrained
</details> <details> <summary><strong>Manopt</strong></summary>
- Local Methods
- First order
- Second order
- Zeroth order
- Box Constraints
- Constrained 🟡
- Global Methods
- Zeroth order
- Unconstrained
</details> <details> <summary><strong>MathOptInterface</strong></summary>
- Local Methods
- First order
- Second order
- Box Constraints
- Constrained
- Global Methods
- First order
- Second order
- Constrained
</details> <details> <summary><strong>MultistartOptimization</strong></summary>
- Global Methods
- Zeroth order
- First order
- Second order
- Box Constraints
</details> <details> <summary><strong>Metaheuristics</strong></summary>
- Global Methods
- Zeroth order
- Unconstrained
- Box Constraints
</details> <details> <summary><strong>NOMAD</strong></summary>
- Global Methods
- Zeroth order
- Unconstrained
- Box Constraints
- Constrained 🟡
</details> <details> <summary><strong>NLopt</strong></summary>
- Local Methods
- First order
- Zeroth order
- Second order 🟡
- Box Constraints
- Local Constrained 🟡
- Global Methods
- Zeroth order
- First order
- Unconstrained
- Constrained 🟡
</details> <details> <summary><strong>Optim</strong></summary>
- Local Methods
- Zeroth order
- First order
- Second order
- Box Constraints
- Constrained
- Global Methods
- Zeroth order
- Unconstrained
- Box Constraints
</details> <details> <summary><strong>PRIMA</strong></summary>
- Local Methods
- Derivative-Free: ✅
- Constraints
- Box Constraints: ✅
- Local Constrained: ✅
</details> <details> <summary><strong>QuadDIRECT</strong></summary>
- Constraints
- Box Constraints: ✅
- Global Methods
- Unconstrained: ✅
</details> 🟡 = 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`
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[b6b21f68] Ipopt v1.6.6
[c8e1da08] IterTools v1.10.0
[2ddba703] Juniper v0.9.2
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⌅ [0fc0a36d] Manopt v0.4.69
[961ee093] ModelingToolkit v9.36.0
[a4795742] NLPModels v0.21.3
[7998695d] NLPModelsTest v0.10.1
⌅ [76087f3c] NLopt v0.6.5
[7f7a1694] Optimization v3.28.0 `~/work/Optimization.jl/Optimization.jl`
[3e6eede4] OptimizationBBO v0.3.0 `../lib/OptimizationBBO`
⌅ [bca83a33] OptimizationBase v1.5.0
[bd407f91] OptimizationCMAEvolutionStrategy v0.2.1 `../lib/OptimizationCMAEvolutionStrategy`
[cb963754] OptimizationEvolutionary v0.3.0 `../lib/OptimizationEvolutionary`
[253f991c] OptimizationFlux v0.2.1 `../lib/OptimizationFlux`
[6f0a0517] OptimizationGCMAES v0.2.0 `../lib/OptimizationGCMAES`
[fd9f6733] OptimizationMOI v0.4.3 `../lib/OptimizationMOI`
[e57b7fff] OptimizationManopt v0.0.3 `../lib/OptimizationManopt`
[3aafef2f] OptimizationMetaheuristics v0.2.0 `../lib/OptimizationMetaheuristics`
[e4316d97] OptimizationMultistartOptimization v0.2.0 `../lib/OptimizationMultistartOptimization`
[064b21be] OptimizationNLPModels v0.0.1 `../lib/OptimizationNLPModels`
[4e6fcdb7] OptimizationNLopt v0.2.2 `../lib/OptimizationNLopt`
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[36348300] OptimizationOptimJL v0.3.2 `../lib/OptimizationOptimJL`
[42dfb2eb] OptimizationOptimisers v0.2.1 `../lib/OptimizationOptimisers`
[72f8369c] OptimizationPRIMA v0.2.0 `../lib/OptimizationPRIMA`
[500b13db] OptimizationPolyalgorithms v0.2.1 `../lib/OptimizationPolyalgorithms`
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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 1.10.5
Commit 6f3fdf7b362 (2024-08-27 14:19 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
LIBM: libopenlibm
LLVM: libLLVM-15.0.7 (ORCJIT, znver3)
Threads: 1 default, 0 interactive, 1 GC (on 4 virtual cores)A more complete overview of all dependencies and their versions is also provided.
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[7e49a35a] RuntimeGeneratedFunctions v0.5.13
[94e857df] SIMDTypes v0.1.0
[476501e8] SLEEFPirates v0.6.43
[322a6be2] Sass v0.2.0
[0bca4576] SciMLBase v2.52.0
[c0aeaf25] SciMLOperators v0.3.10
[1ed8b502] SciMLSensitivity v7.66.1
[53ae85a6] SciMLStructures v1.5.0
[6c6a2e73] Scratch v1.2.1
[eb7571c6] SearchSpaces v0.2.0
[efcf1570] Setfield v1.1.1
[605ecd9f] ShowCases v0.1.0
[777ac1f9] SimpleBufferStream v1.1.0
[727e6d20] SimpleNonlinearSolve v1.12.0
[699a6c99] SimpleTraits v0.9.4
[ce78b400] SimpleUnPack v1.1.0
[47aef6b3] SimpleWeightedGraphs v1.4.0
[66db9d55] SnoopPrecompile v1.0.3
[ed01d8cd] Sobol v1.5.0
[a2af1166] SortingAlgorithms v1.2.1
[47a9eef4] SparseDiffTools v2.20.0
[dc90abb0] SparseInverseSubset v0.1.2
[0a514795] SparseMatrixColorings v0.4.0
[e56a9233] Sparspak v0.3.9
[d4ead438] SpatialIndexing v0.1.6
[276daf66] SpecialFunctions v2.4.0
[f1835b91] SpeedMapping v0.3.0
[171d559e] SplittablesBase v0.1.15
[cae243ae] StackViews v0.1.1
[aedffcd0] Static v1.1.1
[0d7ed370] StaticArrayInterface v1.8.0
[90137ffa] StaticArrays v1.9.7
[1e83bf80] StaticArraysCore v1.4.3
[82ae8749] StatsAPI v1.7.0
[2913bbd2] StatsBase v0.34.3
[4c63d2b9] StatsFuns v1.3.1
[7792a7ef] StrideArraysCore v0.5.7
[09ab397b] StructArrays v0.6.18
[53d494c1] StructIO v0.3.1
[4297ee4d] SymbolicAnalysis v0.3.0
[2efcf032] SymbolicIndexingInterface v0.3.29
[19f23fe9] SymbolicLimits v0.2.2
[d1185830] SymbolicUtils v3.6.0
[0c5d862f] Symbolics v6.6.0
[3783bdb8] TableTraits v1.0.1
[bd369af6] Tables v1.12.0
[62fd8b95] TensorCore v0.1.1
[8ea1fca8] TermInterface v2.0.0
[5d786b92] TerminalLoggers v0.1.7
[1c621080] TestItems v1.0.0
[8290d209] ThreadingUtilities v0.5.2
[a759f4b9] TimerOutputs v0.5.24
[0796e94c] Tokenize v0.5.29
[9f7883ad] Tracker v0.2.35
[3bb67fe8] TranscodingStreams v0.11.2
⌃ [28d57a85] Transducers v0.4.80
[d5829a12] TriangularSolve v0.2.1
[410a4b4d] Tricks v0.1.9
[781d530d] TruncatedStacktraces v1.4.0
[6dd1b50a] Tulip v0.9.6
⌅ [c3b1956e] TypeUtils v0.3.8
[5c2747f8] URIs v1.5.1
[3a884ed6] UnPack v1.0.2
[1986cc42] Unitful v1.21.0
[a7c27f48] Unityper v0.1.6
[013be700] UnsafeAtomics v0.2.1
[d80eeb9a] UnsafeAtomicsLLVM v0.2.1
[3d5dd08c] VectorizationBase v0.21.70
[19fa3120] VertexSafeGraphs v0.2.0
[e88e6eb3] Zygote v0.6.70
[700de1a5] ZygoteRules v0.2.5
[ae81ac8f] ASL_jll v0.1.3+0
[6e34b625] Bzip2_jll v1.0.8+1
[7cc45869] Enzyme_jll v0.0.148+0
[2e619515] Expat_jll v2.6.2+0
[f5851436] FFTW_jll v3.3.10+0
⌃ [f8c6e375] Git_jll v2.36.1+2
[528830af] Gumbo_jll v0.10.2+0
[8fd58aa0] HiGHS_jll v1.7.2+0
[e33a78d0] Hwloc_jll v2.11.1+0
[1d5cc7b8] IntelOpenMP_jll v2024.2.1+0
[9cc047cb] Ipopt_jll v300.1400.1600+0
[dad2f222] LLVMExtra_jll v0.0.33+0
[81d17ec3] L_BFGS_B_jll v3.0.1+0
[94ce4f54] Libiconv_jll v1.17.0+0
[d00139f3] METIS_jll v5.1.2+0
[856f044c] MKL_jll v2024.2.0+0
⌅ [d7ed1dd3] MUMPS_seq_jll v500.700.300+0
[079eb43e] NLopt_jll v2.8.0+0
[2fc7fd02] NOMAD_jll v4.3.1+0
⌅ [656ef2d0] OpenBLAS32_jll v0.3.24+0
⌅ [9bd350c2] OpenSSH_jll v8.9.0+1
⌅ [458c3c95] OpenSSL_jll v1.1.23+0
[efe28fd5] OpenSpecFun_jll v0.5.5+0
[eead6e0c] PRIMA_jll v0.7.1+0
⌅ [f50d1b31] Rmath_jll v0.4.3+0
[319450e9] SPRAL_jll v2024.5.8+0
[47bcb7c8] libsass_jll v3.6.6+0
[1317d2d5] oneTBB_jll v2021.12.0+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 v1.10.0
[4607b0f0] SuiteSparse
[fa267f1f] TOML v1.0.3
[a4e569a6] Tar v1.10.0
[8dfed614] Test
[cf7118a7] UUIDs
[4ec0a83e] Unicode
[e66e0078] CompilerSupportLibraries_jll v1.1.1+0
[deac9b47] LibCURL_jll v8.4.0+0
[e37daf67] LibGit2_jll v1.6.4+0
[29816b5a] LibSSH2_jll v1.11.0+1
[c8ffd9c3] MbedTLS_jll v2.28.2+1
[14a3606d] MozillaCACerts_jll v2023.1.10
[4536629a] OpenBLAS_jll v0.3.23+4
[05823500] OpenLibm_jll v0.8.1+2
[efcefdf7] PCRE2_jll v10.42.0+1
[bea87d4a] SuiteSparse_jll v7.2.1+1
[83775a58] Zlib_jll v1.2.13+1
[8e850b90] libblastrampoline_jll v5.11.0+0
[8e850ede] nghttp2_jll v1.52.0+1
[3f19e933] p7zip_jll v17.4.0+2
Info Packages marked with ⌃ and ⌅ have new versions available. Those with ⌃ may be upgradable, but those with ⌅ are restricted by compatibility constraints from upgrading. To see why use `status --outdated -m`You can also download the manifest file and the project file.