Optimization on a Finer Scale: Bounded Local Subgradient Variation Perspective

arXiv:2403.16317v1 Announce Type: cross
Abstract: We initiate the study of nonsmooth optimization problems under bounded local subgradient variation, which postulates bounded difference between (sub)gradients in small local regions around points, in either average or maximum sense. The resulting class of objective functions encapsulates the classes of objective functions traditionally studied in optimization, which are defined based on either Lipschitz continuity of the objective or H\"{o}lder/Lipschitz continuity of its gradient. Further, the defined class contains functions that are neither Lipschitz continuous …

abstract arxiv class cs.ds cs.lg difference functions math.oc optimization perspective scale sense small study type variation