DiffOpt.jl is a package for differentiating convex optimization programs with respect to the program parameters. DiffOpt currently supports linear, quadratic, and conic programs.
DiffOpt.jl is licensed under the
MIT License.
Install DiffOpt using Pkg.add:
import Pkg Pkg.add("DiffOpt")
The documentation for DiffOpt.jl includes a detailed description of the theory behind the package, along with examples, tutorials, and an API reference.
Here is an example with a Parametric Linear Program:
using JuMP, DiffOpt, HiGHS model = DiffOpt.quadratic_diff_model(HiGHS.Optimizer) set_silent(model) p_val = 4.0 pc_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. p direction_p = 3.0 DiffOpt.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 pc p_val = 2.0 pc_val = 6.0 set_parameter_value(p, p_val) set_parameter_value(pc, pc_val) # re-optimize optimize!(model) # check solution @show value(x) ≈ 3 * p_val / pc_val # stop differentiating with respect to p DiffOpt.empty_input_sensitivities!(model) # differentiate w.r.t. pc direction_pc = 10.0 DiffOpt.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 sensitivities DiffOpt.empty_input_sensitivities!(model) # Now, reverse model AD direction_x = 10.0 DiffOpt.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)
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.
DiffOpt began as a NumFOCUS sponsored Google Summer of Code (2020) project