DiffOpt.jl

DiffOpt.jl is a package for differentiating convex optimization programs with respect to the program parameters. DiffOpt currently supports linear, quadratic, and conic programs.

License

DiffOpt.jl is licensed under the MIT License.

Installation

Install DiffOpt using Pkg.add:

import PkgPkg.add("DiffOpt")

Documentation

The documentation for DiffOpt.jl includes a detailed description of the theory behind the package, along with examples, tutorials, and an API reference.

Use with JuMP

DiffOpt-JuMP API with Parameters

Here is an example with a Parametric Linear Program:

using JuMP, DiffOpt, HiGHSmodel = DiffOpt.quadratic_diff_model(HiGHS.Optimizer)set_silent(model)p_val = 4.0pc_val = 2.0@variable(model, x)@variable(model, p in Parameter(p_val))@variable(model, pc in Parameter(pc_val))@constraint(model, cons, pc * x >= 3 * p)@objective(model, Min, 2x)optimize!(model)@show value(x) == 3 * p_val / pc_val# the function is# x(p, pc) = 3p / pc# hence,# dx/dp = 3 / pc# dx/dpc = -3p / pc^2# First, try forward mode AD# differentiate w.r.t. pdirection_p = 3.0DiffOpt.set_forward_parameter(model, p, direction_p)DiffOpt.forward_differentiate!(model)@show DiffOpt.get_forward_variable(model, x) == direction_p * 3 / pc_val# update p and pcp_val = 2.0pc_val = 6.0set_parameter_value(p, p_val)set_parameter_value(pc, pc_val)# re-optimizeoptimize!(model)# check solution@show value(x) ≈ 3 * p_val / pc_val# stop differentiating with respect to pDiffOpt.empty_input_sensitivities!(model)# differentiate w.r.t. pcdirection_pc = 10.0DiffOpt.set_forward_parameter(model, pc, direction_pc)DiffOpt.forward_differentiate!(model)@show abs(DiffOpt.get_forward_variable(model, x) -    -direction_pc * 3 * p_val / pc_val^2) < 1e-5# always a good practice to clear previously set sensitivitiesDiffOpt.empty_input_sensitivities!(model)# Now, reverse model ADdirection_x = 10.0DiffOpt.set_reverse_variable(model, x, direction_x)DiffOpt.reverse_differentiate!(model)@show DiffOpt.get_reverse_parameter(model, p) == direction_x * 3 / pc_val@show DiffOpt.get_reverse_parameter(model, pc) == -direction_x * 3 * p_val / pc_val^2

Available models:

• DiffOpt.quadratic_diff_model: Quadratic Programs (QP) and Linear Programs

(LP)

• DiffOpt.conic_diff_model: Conic Programs (CP) and Linear Programs (LP)
• DiffOpt.nonlinear_diff_model: Nonlinear Programs (NLP), Quadratic Program

(QP) and Linear Programs (LP)

• DiffOpt.diff_model: Nonlinear Programs (NLP), Conic Programs (CP),

Quadratic Programs (QP) and Linear Programs (LP)

Citing DiffOpt.jl

If you find DiffOpt.jl useful in your work, we kindly request that you cite the following paper:

@article{besancon2023diffopt,
    title={Flexible Differentiable Optimization via Model Transformations},
    author={Besançon, Mathieu and Dias Garcia, Joaquim and Legat, Beno{\^\i}t and Sharma, Akshay},
    journal={INFORMS Journal on Computing},
    year={2023},
    volume={36},
    number={2},
    pages={456--478},
    doi={10.1287/ijoc.2022.0283},
    publisher={INFORMS}
}

A preprint of this paper is freely available.

GSOC2020

DiffOpt began as a NumFOCUS sponsored Google Summer of Code (2020) project