2022/12/15 by Jérôme Bolte, Edouard Pauwels, Bolte, Jérôme +3 · 2 citations
Computer Science · Mathematics · Medicine · #Advanced Optimization Algorithms Research #Bone and Joint Diseases #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Optimization and Control (math.OC) #Optimization and Variational Analysis
paper · doi:10.48550/arxiv.2212.07844
openalex publication_date 2022/12/15 · openalex created_date 2022/12/28 · openalex updated_date 2026/07/28
We leverage path differentiability and a recent result on nonsmooth implicit differentiation calculus to give sufficient conditions ensuring that the solution to a monotone inclusion problem will be path differentiable, with formulas for computing its generalized gradient. A direct consequence of our result is that these solutions happen to be differentiable almost everywhere. Our approach is fully compatible with automatic differentiation and comes with assumptions which are easy to check, roughly speaking: semialgebraicity and strong monotonicity. We illustrate the scope of our results by considering three fundamental composite problem settings: strongly convex problems, dual solutions to convex minimization problems and primal-dual solutions to min-max problems.