Automatic Differentiation Construction Choice Recommendations

AutoForwardDiff{chunksize} <: AbstractADType

An AbstractADType choice for use in OptimizationFunction for automatically generating the unspecified derivative functions. Usage:

OptimizationFunction(f, AutoForwardDiff(); kwargs...)

This uses the ForwardDiff.jl package. It is the fastest choice for small systems, especially with heavy scalar interactions. It is easy to use and compatible with most Julia functions which have loose type restrictions. However, because it's forward-mode, it scales poorly in comparison to other AD choices. Hessian construction is suboptimal as it uses the forward-over-forward approach.

• Compatible with GPUs
• Compatible with Hessian-based optimization
• Compatible with Hv-based optimization
• Compatible with constraints

Note that only the unspecified derivative functions are defined. For example, if a hess function is supplied to the OptimizationFunction, then the Hessian is not defined via ForwardDiff.

AutoFiniteDiff{T1,T2,T3} <: AbstractADType

An AbstractADType choice for use in OptimizationFunction for automatically generating the unspecified derivative functions. Usage:

OptimizationFunction(f, AutoFiniteDiff(); kwargs...)

This uses FiniteDiff.jl. While not necessarily the most efficient, this is the only choice that doesn't require the f function to be automatically differentiable, which means it applies to any choice. However, because it's using finite differencing, one needs to be careful as this procedure introduces numerical error into the derivative estimates.

• Compatible with GPUs
• Compatible with Hessian-based optimization
• Compatible with Hv-based optimization
• Compatible with constraint functions

Note that only the unspecified derivative functions are defined. For example, if a hess function is supplied to the OptimizationFunction, then the Hessian is not defined via FiniteDiff.

Constructor

AutoFiniteDiff(; fdtype = Val(:forward)fdjtype = fdtype, fdhtype = Val(:hcentral))

• fdtype: the method used for defining the gradient
• fdjtype: the method used for defining the Jacobian of constraints.
• fdhtype: the method used for defining the Hessian

For more information on the derivative type specifiers, see the FiniteDiff.jl documentation.

AutoReverseDiff <: AbstractADType

An AbstractADType choice for use in OptimizationFunction for automatically generating the unspecified derivative functions. Usage:

OptimizationFunction(f, AutoReverseDiff(); kwargs...)

This uses the ReverseDiff.jl package. AutoReverseDiff has a default argument, compile, which denotes whether the reverse pass should be compiled. compile should only be set to true if f contains no branches (if statements, while loops) otherwise it can produce incorrect derivatives!

AutoReverseDiff is generally applicable to many pure Julia codes, and with compile=true it is one of the fastest options on code with heavy scalar interactions. Hessian calculations are fast by mixing ForwardDiff with ReverseDiff for forward-over-reverse. However, its performance can falter when compile=false.

• Not compatible with GPUs
• Compatible with Hessian-based optimization by mixing with ForwardDiff
• Compatible with Hv-based optimization by mixing with ForwardDiff
• Not compatible with constraint functions

Note that only the unspecified derivative functions are defined. For example, if a hess function is supplied to the OptimizationFunction, then the Hessian is not defined via ReverseDiff.

Constructor

AutoReverseDiff(; compile = false)

Note: currently, compilation is not defined/used!

AutoZygote <: AbstractADType

An AbstractADType choice for use in OptimizationFunction for automatically generating the unspecified derivative functions. Usage:

OptimizationFunction(f, AutoZygote(); kwargs...)

This uses the Zygote.jl package. This is the staple reverse-mode AD that handles a large portion of Julia with good efficiency. Hessian construction is fast via forward-over-reverse mixing ForwardDiff.jl with Zygote.jl

• Compatible with GPUs
• Compatible with Hessian-based optimization via ForwardDiff
• Compatible with Hv-based optimization via ForwardDiff
• Not compatible with constraint functions

Note that only the unspecified derivative functions are defined. For example, if a hess function is supplied to the OptimizationFunction, then the Hessian is not defined via Zygote.

AutoTracker <: AbstractADType

An AbstractADType choice for use in OptimizationFunction for automatically generating the unspecified derivative functions. Usage:

OptimizationFunction(f, AutoTracker(); kwargs...)

This uses the Tracker.jl package. Generally slower than ReverseDiff, it is generally applicable to many pure Julia codes.

• Compatible with GPUs
• Not compatible with Hessian-based optimization
• Not compatible with Hv-based optimization
• Not compatible with constraint functions

Note that only the unspecified derivative functions are defined. For example, if a hess function is supplied to the OptimizationFunction, then the Hessian is not defined via Tracker.

AutoModelingToolkit <: AbstractADType

An AbstractADType choice for use in OptimizationFunction for automatically generating the unspecified derivative functions. Usage:

OptimizationFunction(f, AutoModelingToolkit(); kwargs...)

This uses the ModelingToolkit.jl package's modelingtookitize functionality to generate the derivatives and other fields of an OptimizationFunction. This backend creates the symbolic expressions for the objective and its derivatives as well as the constraints and their derivatives. Through structural_simplify, it enforces simplifications that can reduce the number of operations needed to compute the derivatives of the constraints. This automatically generates the expression graphs that some solver interfaces through OptimizationMOI like AmplNLWriter.jl require.

• Compatible with GPUs
• Compatible with Hessian-based optimization
• Compatible with Hv-based optimization
• Compatible with constraints

Note that only the unspecified derivative functions are defined. For example, if a hess function is supplied to the OptimizationFunction, then the Hessian is not generated via ModelingToolkit.

Constructor

AutoModelingToolkit(false, false)

• obj_sparse: to indicate whether the objective hessian is sparse.
• cons_sparse: to indicate whether the constraints' jacobian and hessian are sparse.

AutoEnzyme <: AbstractADType

An AbstractADType choice for use in OptimizationFunction for automatically generating the unspecified derivative functions. Usage:

OptimizationFunction(f, AutoEnzyme(); kwargs...)

This uses the Enzyme.jl package. Enzyme performs automatic differentiation on the LLVM IR code generated from julia. It is highly-efficient and its ability perform AD on optimized code allows Enzyme to meet or exceed the performance of state-of-the-art AD tools.

• Compatible with GPUs
• Compatible with Hessian-based optimization
• Compatible with Hv-based optimization
• Compatible with constraints

Note that only the unspecified derivative functions are defined. For example, if a hess function is supplied to the OptimizationFunction, then the Hessian is not defined via Enzyme.