Differentiating Nonsmooth Solutions to Parametric Monotone Inclusion Problems
利用路径可微性和非光滑隐式微分，给出了单调包含问题解路径可微的充分条件及其广义梯度公式，适用于强凸问题、对偶解和极小极大问题的原对偶解。
We leverage path differentiability and a recent result on nonsmooth implicit\ndifferentiation calculus to give sufficient conditions ensuring that the\nsolution to a monotone inclusion problem will be path differentiable, with\nformulas for computing its generalized gradient. A direct consequence of our\nresult is that these solutions happen to be differentiable almost everywhere.\nOur approach is fully compatible with automatic differentiation and comes with\nassumptions which are easy to check, roughly speaking: semialgebraicity and\nstrong monotonicity. We illustrate the scope of our results by considering\nthree fundamental composite problem settings: strongly convex problems, dual\nsolutions to convex minimization problems and primal-dual solutions to min-max\nproblems.\n