Fixed-Point Automatic Differentiation of Forward--Backward Splitting Algorithms for Partly Smooth Functions. (arXiv:2208.03107v1 [math.OC])

A large class of non-smooth practical optimization problems can be written as
minimization of a sum of smooth and partly smooth functions. We consider such
structured problems which also depend on a parameter vector and study the
problem of differentiating its solution mapping with respect to the parameter
which has far reaching applications in sensitivity analysis and parameter
learning optmization problems. We show that under partial smoothness and other
mild assumptions, Automatic Differentiation (AD) of the sequence generated by
proximal …

algorithms arxiv differentiation fixed-point math