Differentiating convex optimization program w.r.t. program parameters
Author jump-dev
47 Stars
Updated Last
1 Month Ago
Started In
May 2020


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Differentiating convex optimization program (JuMP.jl or MathOptInterface.jl models) with respect to program parameters. Currently supports LPs, QPs.


DiffOpt can be installed through the Julia package manager:

(v1.3) pkg> add https://github.com/jump-dev/DiffOpt.jl


Create a differentiable model from existing optimizers:

using DiffOpt
using GLPK
using MathOptInterface
const MOI = MathOptInterface

diff = diff_optimizer(GLPK.Optimizer)

Update and solve the model:

x = MOI.add_variables(diff, 2)
c = MOI.add_constraint(diff, ...)


Finally, differentiate the model (primal and dual variables specifically) to obtain product of jacobians with respect to problem parameters and a backward pass vector.

Currently, DiffOpt supports two backends. If the optimization problem is of quadratic form i.e.

minimize_z z^T Q z / 2 + q^T z
subject to: Az = b,
            Gz ≤ h

then one can compute gradients by providing a backward pass vector

bpv = [1.0, 1.0]
grads = backward(diff, ["Q", "q", "h"], bpv)

Secondly, for a conic problem of the format:

minimize_x c^T x
subject to: Ax + b in K


  • the objective is linear
  • K is a Cartesian product of linear, semidefinite, second-order cones then one can compute gradients by providing perturbations
grads = backward(diff, dA, db, dc)