RIS ID
143425
Abstract
2020 Society for Industrial and Applied Mathematics. We construct a proximal average for two prox-bounded functions, which recovers the classical proximal average for two convex functions. The new proximal average transforms continuously in epi-topology from one proximal hull to the other. When one of the functions is differentiable, the new proximal average is differentiable. We give characterizations for Lipschitz and single-valued proximal mappings and we show that the convex combination of convexified proximal mappings is always a proximal mapping. Subdifferentiability and behaviors of infimal values and minimizers are also studied.
Publication Details
Chen, J., Wang, X. & Planiden, C. (2020). A proximal average for prox-bounded functions. SIAM Journal on Optimization, 30 (2), 1366-1390.