  We view a conic optimization problem that has a unique solution as a map from
its data to its solution. If sufficient regularity conditions hold at a
solution point, namely that the implicit function theorem applies to the
normalized residual function of [Busseti et al., 2018], the problem solution
map is differentiable. We obtain the derivative, in the form of an abstract
linear operator. This applies to any convex optimization problem in conic form,
while a previous result [Amos et al., 2016] studied strictly convex quadratic
programs. Such differentiable problems can be used, for example, in machine
learning, control, and related areas, as a layer in an end-to-end learning and
control procedure, for backpropagation. We accompany this note with a
lightweight Python implementation which can handle problems with the cone
constraints commonly used in practice.
