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🚀 Add NonLinearProgram Support to DiffOpt.jl (#260)
* NonLinearProgram * index by MOI index * only cache gradient * update API * start reverse mode * add overloads * update MOI wrapper * update code for DiffOpt API * working code * usage example * add reverse diff * update code * update tests * update tests * add forward_differentiate! tests * add reverse_differentiate! tests * update docs * format * update API reference * fix typos * update reference * update spdiagm * Typo "acutal" to "actual" (#258) Correcting typo "acutal" to "actual" * Fix GitHub actions badge in README (#263) * Implement MOI.Utilities.scalar_type for (Matrix|Sparse)VectorAffineFunction (#264) * Use SlackBridgePrimalDualStart (#253) * Use SlackBridgePrimalDualStart * Update src/copy_dual.jl * Remove test_broken * Add supports * Add comment * Move to AbstractModel * Integrate with POI to improve UX (#262) * [WIP] Integrate with POI to improve UX * add missing import * temp change to proj toml * format * simplify method setting to sue model constructor * add possible fix to scalarize bridge error * add pkg to project * format * improvements * remove jump wrapper * clean tests * fix readme * use intermediary API * format * Apply suggestions from code review Co-authored-by: Benoît Legat <[email protected]> * add suggestion * use Parameter set * todo was fixed * format * update docs for newer Flux * format * kwargs * remove diff model * suggestions * format * fix examples --------- Co-authored-by: Benoît Legat <[email protected]> * Add error for missing starting value (#269) * update API * expose kwargs * restrict hessian type * reverse wrong change * update usage * fix mad merge * fix typo * fix typo * fix wrong index * reverse index * allow user to just set relevat sensitivities * fix copy reverse sensitivity dual * format * update tests * format * update docs * extend parameter @test_throws tests for NLP * update comments * update private api: _add_leq_geq * fix typo * continue fix typo check asserts * expose factorization through as MOI.AbstractModelAttribute * add tests factorization * add comment * rm rm kwargs * use correct underscore signature for private funcs * format * change github actions to v3 * reverse checkout version * add reference sipopt paper * update factorization routine API * format * Update ci.yml * improve coverage * add test inertia correction * add test ReverseConstraintDual * format * rm useless checks * add test get ReverseConstraintDual * format * rm unecessary funcs * rm kwargs * format * rename factorization attributte * add supports * Apply suggestions from code review --------- Co-authored-by: mzagorowska <[email protected]> Co-authored-by: Oscar Dowson <[email protected]> Co-authored-by: Benoît Legat <[email protected]> Co-authored-by: Joaquim <[email protected]>
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Diff for: ‎.github/workflows/ci.yml

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with:
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version: ${{ matrix.version }}
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arch: ${{ matrix.arch }}
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- uses: actions/cache@v1
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- uses: actions/cache@v3
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env:
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cache-name: cache-artifacts
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with:

Diff for: ‎Project.toml

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name = "DiffOpt"
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uuid = "930fe3bc-9c6b-11ea-2d94-6184641e85e7"
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authors = ["Akshay Sharma", "Mathieu Besançon", "Joaquim Dias Garcia", "Benoît Legat", "Oscar Dowson"]
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version = "0.4.3"
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authors = ["Akshay Sharma", "Mathieu Besançon", "Joaquim Dias Garcia", "Benoît Legat", "Oscar Dowson", "Andrew Rosemberg"]
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version = "0.5.0"
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[deps]
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BlockDiagonals = "0a1fb500-61f7-11e9-3c65-f5ef3456f9f0"

Diff for: ‎docs/src/index.md

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# DiffOpt.jl
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[DiffOpt.jl](https://github.com/jump-dev/DiffOpt.jl) is a package for differentiating convex optimization program ([JuMP.jl](https://github.com/jump-dev/JuMP.jl) or [MathOptInterface.jl](https://github.com/jump-dev/MathOptInterface.jl) models) with respect to program parameters. Note that this package does not contain any solver.
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[DiffOpt.jl](https://github.com/jump-dev/DiffOpt.jl) is a package for differentiating convex and non-convex optimization program ([JuMP.jl](https://github.com/jump-dev/JuMP.jl) or [MathOptInterface.jl](https://github.com/jump-dev/MathOptInterface.jl) models) with respect to program parameters. Note that this package does not contain any solver.
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This package has two major backends, available via the `reverse_differentiate!` and `forward_differentiate!` methods, to differentiate models (quadratic or conic) with optimal solutions.
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!!! note
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Currently supports *linear programs* (LP), *convex quadratic programs* (QP) and *convex conic programs* (SDP, SOCP, exponential cone constraints only).
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Currently supports *linear programs* (LP), *convex quadratic programs* (QP), *convex conic programs* (SDP, SOCP, exponential cone constraints only), and *general nonlinear programs* (NLP).
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## Installation
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## Why are Differentiable optimization problems important?
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Differentiable optimization is a promising field of convex optimization and has many potential applications in game theory, control theory and machine learning (specifically deep learning - refer [this video](https://www.youtube.com/watch?v=NrcaNnEXkT8) for more).
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Recent work has shown how to differentiate specific subclasses of convex optimization problems. But several applications remain unexplored (refer section 8 of this [really good thesis](https://github.com/bamos/thesis)). With the help of automatic differentiation, differentiable optimization can have a significant impact on creating end-to-end differentiable systems to model neural networks, stochastic processes, or a game.
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Differentiable optimization is a promising field of constrained optimization and has many potential applications in game theory, control theory and machine learning (specifically deep learning - refer [this video](https://www.youtube.com/watch?v=NrcaNnEXkT8) for more).
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Recent work has shown how to differentiate specific subclasses of constrained optimization problems. But several applications remain unexplored (refer section 8 of this [really good thesis](https://github.com/bamos/thesis)). With the help of automatic differentiation, differentiable optimization can have a significant impact on creating end-to-end differentiable systems to model neural networks, stochastic processes, or a game.
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## Contributing

Diff for: ‎docs/src/manual.md

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# Manual
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!!! note
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As of now, this package only works for optimization models that can be written either in convex conic form or convex quadratic form.
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## Supported objectives & constraints - `QuadraticProgram` backend
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## Supported objectives & constraints - scheme 1
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For `QuadraticProgram` backend, the package supports following `Function-in-Set` constraints:
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Other conic sets such as `RotatedSecondOrderCone` and `PositiveSemidefiniteConeSquare` are supported through bridges.
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## Supported objectives & constraints - `NonlinearProgram` backend
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For the `NonlinearProgram` backend, the package supports following `Function-in-Set` constraints:
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| MOI Function | MOI Set |
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|:-------|:---------------|
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| `VariableIndex` | `GreaterThan` |
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| `VariableIndex` | `LessThan` |
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| `VariableIndex` | `EqualTo` |
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| `ScalarAffineFunction` | `GreaterThan` |
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| `ScalarAffineFunction` | `LessThan` |
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| `ScalarAffineFunction` | `EqualTo` |
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| `ScalarQuadraticFunction` | `GreaterThan` |
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| `ScalarQuadraticFunction` | `LessThan` |
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| `ScalarQuadraticFunction` | `EqualTo` |
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| `ScalarNonlinearFunction` | `GreaterThan` |
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| `ScalarNonlinearFunction` | `LessThan` |
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| `ScalarNonlinearFunction` | `EqualTo` |
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and the following objective types:
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| MOI Function |
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|:-------:|
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| `VariableIndex` |
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| `ScalarAffineFunction` |
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| `ScalarQuadraticFunction` |
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| `ScalarNonlinearFunction` |
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## Creating a differentiable MOI optimizer
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## Conic problem formulation
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!!! note
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As of now, the package is using `SCS` geometric form for affine expressions in cones.
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As of now, when defining a conic or convex quadratic problem, the package is using `SCS` geometric form for affine expressions in cones.
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Consider a convex conic optimization problem in its primal (P) and dual (D) forms:
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```math

Diff for: ‎docs/src/reference.md

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```
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```@autodocs
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Modules = [DiffOpt, DiffOpt.QuadraticProgram, DiffOpt.ConicProgram]
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Modules = [DiffOpt, DiffOpt.QuadraticProgram, DiffOpt.ConicProgram, DiffOpt.NonLinearProgram]
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```

Diff for: ‎docs/src/usage.md

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DiffOpt.forward_differentiate!(model)
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grad_x = MOI.get.(model, DiffOpt.ForwardVariablePrimal(), x)
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```
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3. To differentiate a general nonlinear program, have to use the API for Parameterized JuMP models. For example, consider the following nonlinear program:
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```julia
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using JuMP, DiffOpt, HiGHS
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model = Model(() -> DiffOpt.diff_optimizer(Ipopt.Optimizer))
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set_silent(model)
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p_val = 4.0
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pc_val = 2.0
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@variable(model, x)
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@variable(model, p in Parameter(p_val))
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@variable(model, pc in Parameter(pc_val))
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@constraint(model, cons, pc * x >= 3 * p)
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@objective(model, Min, x^4)
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optimize!(model)
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@show value(x) == 3 * p_val / pc_val
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# the function is
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# x(p, pc) = 3p / pc
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# hence,
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# dx/dp = 3 / pc
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# dx/dpc = -3p / pc^2
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# First, try forward mode AD
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# differentiate w.r.t. p
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direction_p = 3.0
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MOI.set(model, DiffOpt.ForwardConstraintSet(), ParameterRef(p), Parameter(direction_p))
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DiffOpt.forward_differentiate!(model)
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@show MOI.get(model, DiffOpt.ForwardVariablePrimal(), x) == direction_p * 3 / pc_val
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# update p and pc
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p_val = 2.0
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pc_val = 6.0
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set_parameter_value(p, p_val)
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set_parameter_value(pc, pc_val)
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# re-optimize
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optimize!(model)
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# check solution
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@show value(x) ≈ 3 * p_val / pc_val
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# stop differentiating with respect to p
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DiffOpt.empty_input_sensitivities!(model)
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# differentiate w.r.t. pc
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direction_pc = 10.0
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MOI.set(model, DiffOpt.ForwardConstraintSet(), ParameterRef(pc), Parameter(direction_pc))
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DiffOpt.forward_differentiate!(model)
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@show abs(MOI.get(model, DiffOpt.ForwardVariablePrimal(), x) -
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-direction_pc * 3 * p_val / pc_val^2) < 1e-5
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# always a good practice to clear previously set sensitivities
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DiffOpt.empty_input_sensitivities!(model)
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# Now, reverse model AD
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direction_x = 10.0
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MOI.set(model, DiffOpt.ReverseVariablePrimal(), x, direction_x)
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DiffOpt.reverse_differentiate!(model)
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@show MOI.get(model, DiffOpt.ReverseConstraintSet(), ParameterRef(p)) == MOI.Parameter(direction_x * 3 / pc_val)
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@show abs(MOI.get(model, DiffOpt.ReverseConstraintSet(), ParameterRef(pc)).value -
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-direction_x * 3 * p_val / pc_val^2) < 1e-5
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```

Diff for: ‎src/DiffOpt.jl

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include("QuadraticProgram/QuadraticProgram.jl")
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include("ConicProgram/ConicProgram.jl")
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include("NonLinearProgram/NonLinearProgram.jl")
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"""
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add_all_model_constructors(model)
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function add_all_model_constructors(model)
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add_model_constructor(model, QuadraticProgram.Model)
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add_model_constructor(model, ConicProgram.Model)
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add_model_constructor(model, NonLinearProgram.Model)
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return
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end
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function add_default_factorization(model)
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model.input_cache.factorization =
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NonLinearProgram._lu_with_inertia_correction
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return
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end
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