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. However, you will need to add the specific optimizer 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 Optimizers

Package	Local Gradient-Based	Local Hessian-Based	Local Derivative-Free	Box Constraints	Local Constrained	Global Unconstrained	Global Constrained
BlackBoxOptim	❌	❌	❌	✅	❌	✅	❌ ✅
CMAEvolutionaryStrategy	❌	❌	❌	✅	❌	✅	❌
Evolutionary	❌	❌	❌	✅	❌	✅	🟡
Flux	✅	❌	❌	❌	❌	❌	❌
GCMAES	❌	❌	❌	✅	❌	✅	❌
MathOptInterface	✅	✅	✅	✅	✅	✅	🟡
MultistartOptimization	❌	❌	❌	✅	❌	✅	❌
Metaheuristics	❌	❌	❌	✅	❌	✅	🟡
NOMAD	❌	❌	❌	✅	❌	✅	🟡
NLopt	✅	❌	✅	✅	🟡	✅	🟡
Optim	✅	✅	✅	✅	✅	✅	✅
PRIMA	❌	❌	✅	✅	✅	❌	❌
QuadDIRECT	❌	❌	❌	✅	❌	✅	❌

✅ = supported

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

❌ = not supported

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`
  [7c4d4715] AmplNLWriter v1.2.1
  [e30172f5] Documenter v1.3.0
  [6a86dc24] FiniteDiff v2.23.0
  [587475ba] Flux v0.14.15
  [f6369f11] ForwardDiff v0.10.36
  [87dc4568] HiGHS v1.9.0
  [b6b21f68] Ipopt v1.6.2
  [c8e1da08] IterTools v1.10.0
  [2ddba703] Juniper v0.9.2
  [961ee093] ModelingToolkit v9.6.1
⌅ [76087f3c] NLopt v0.6.5
  [7f7a1694] Optimization v3.24.3 `~/work/Optimization.jl/Optimization.jl`
  [3e6eede4] OptimizationBBO v0.2.1 `../lib/OptimizationBBO`
  [bca83a33] OptimizationBase v0.0.5
  [bd407f91] OptimizationCMAEvolutionStrategy v0.2.1 `../lib/OptimizationCMAEvolutionStrategy`
  [cb963754] OptimizationEvolutionary v0.2.2 `../lib/OptimizationEvolutionary`
  [253f991c] OptimizationFlux v0.2.1 `../lib/OptimizationFlux`
  [6f0a0517] OptimizationGCMAES v0.2.0 `../lib/OptimizationGCMAES`
  [fd9f6733] OptimizationMOI v0.4.2 `../lib/OptimizationMOI`
  [3aafef2f] OptimizationMetaheuristics v0.2.0 `../lib/OptimizationMetaheuristics`
  [e4316d97] OptimizationMultistartOptimization v0.2.0 `../lib/OptimizationMultistartOptimization`
  [4e6fcdb7] OptimizationNLopt v0.2.0 `../lib/OptimizationNLopt`
  [2cab0595] OptimizationNOMAD v0.2.0 `../lib/OptimizationNOMAD`
  [36348300] OptimizationOptimJL v0.2.3 `../lib/OptimizationOptimJL`
  [42dfb2eb] OptimizationOptimisers v0.2.1 `../lib/OptimizationOptimisers`
  [72f8369c] OptimizationPRIMA v0.0.2 `../lib/OptimizationPRIMA`
  [500b13db] OptimizationPolyalgorithms v0.2.0 `../lib/OptimizationPolyalgorithms`
  [3d669222] OptimizationSpeedMapping v0.2.0 `../lib/OptimizationSpeedMapping`
  [1dea7af3] OrdinaryDiffEq v6.74.1
  [37e2e3b7] ReverseDiff v1.15.1
  [0bca4576] SciMLBase v2.30.1
  [1ed8b502] SciMLSensitivity v7.56.2
  [9f7883ad] Tracker v0.2.33
  [e88e6eb3] Zygote v0.6.69
  [9cc047cb] Ipopt_jll v300.1400.1400+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 1.10.2
Commit bd47eca2c8a (2024-03-01 10:14 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.

Status `~/work/Optimization.jl/Optimization.jl/docs/Manifest.toml`
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⌅ [ec485272] ArnoldiMethod v0.2.0
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⌅ [198e06fe] BangBang v0.3.40
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  [a134a8b2] BlackBoxOptim v0.6.3
  [fa961155] CEnum v0.5.0
  [8d3b24bd] CMAEvolutionStrategy v0.2.6
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⌅ [06fc5a27] DynamicQuantities v0.12.3
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⌅ [f151be2c] EnzymeCore v0.6.5
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  [1fa38f19] Format v1.3.6
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⌅ [61eb1bfa] GPUCompiler v0.25.0
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  [bcdb8e00] Metaheuristics v3.3.4
⌅ [128add7d] MicroCollections v0.1.4
  [e1d29d7a] Missings v1.1.0
  [961ee093] ModelingToolkit v9.6.1
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  [3933049c] MultistartOptimization v0.2.2
  [102ac46a] MultivariatePolynomials v0.5.4
  [d8a4904e] MutableArithmetics v1.4.1
  [d41bc354] NLSolversBase v7.8.3
⌅ [76087f3c] NLopt v0.6.5
  [2774e3e8] NLsolve v4.5.1
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  [0b1bfda6] OneHotArrays v0.2.5
  [4d8831e6] OpenSSL v1.4.2
  [429524aa] Optim v1.9.3
  [3bd65402] Optimisers v0.3.2
  [7f7a1694] Optimization v3.24.3 `~/work/Optimization.jl/Optimization.jl`
  [3e6eede4] OptimizationBBO v0.2.1 `../lib/OptimizationBBO`
  [bca83a33] OptimizationBase v0.0.5
  [bd407f91] OptimizationCMAEvolutionStrategy v0.2.1 `../lib/OptimizationCMAEvolutionStrategy`
  [cb963754] OptimizationEvolutionary v0.2.2 `../lib/OptimizationEvolutionary`
  [253f991c] OptimizationFlux v0.2.1 `../lib/OptimizationFlux`
  [6f0a0517] OptimizationGCMAES v0.2.0 `../lib/OptimizationGCMAES`
  [fd9f6733] OptimizationMOI v0.4.2 `../lib/OptimizationMOI`
  [3aafef2f] OptimizationMetaheuristics v0.2.0 `../lib/OptimizationMetaheuristics`
  [e4316d97] OptimizationMultistartOptimization v0.2.0 `../lib/OptimizationMultistartOptimization`
  [4e6fcdb7] OptimizationNLopt v0.2.0 `../lib/OptimizationNLopt`
  [2cab0595] OptimizationNOMAD v0.2.0 `../lib/OptimizationNOMAD`
  [36348300] OptimizationOptimJL v0.2.3 `../lib/OptimizationOptimJL`
  [42dfb2eb] OptimizationOptimisers v0.2.1 `../lib/OptimizationOptimisers`
  [72f8369c] OptimizationPRIMA v0.0.2 `../lib/OptimizationPRIMA`
  [500b13db] OptimizationPolyalgorithms v0.2.0 `../lib/OptimizationPolyalgorithms`
  [3d669222] OptimizationSpeedMapping v0.2.0 `../lib/OptimizationSpeedMapping`
  [bac558e1] OrderedCollections v1.6.3
  [1dea7af3] OrdinaryDiffEq v6.74.1
  [90014a1f] PDMats v0.11.31
⌃ [0a7d04aa] PRIMA v0.1.1
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  [d96e819e] Parameters v0.12.3
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⌃ [28d57a85] Transducers v0.4.80
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  [e33a78d0] Hwloc_jll v2.10.0+0
  [1d5cc7b8] IntelOpenMP_jll v2024.0.2+0
  [9cc047cb] Ipopt_jll v300.1400.1400+0
  [dad2f222] LLVMExtra_jll v0.0.29+0
  [94ce4f54] Libiconv_jll v1.17.0+0
  [d00139f3] METIS_jll v5.1.2+0
  [856f044c] MKL_jll v2024.0.0+0
  [d7ed1dd3] MUMPS_seq_jll v500.600.201+0
  [079eb43e] NLopt_jll v2.7.1+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 v0.4.0+0
  [319450e9] SPRAL_jll v2024.1.18+0
  [47bcb7c8] libsass_jll v3.6.4+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 v1.1.0+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 v5.8.0+1
  [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.