Steepest descent drives both theory and practice of nonsmooth optimization. We study slight relaxations of two influential notions of steepest descent curves — curves of maximal slope and solutions to evolution equations. In particular, we provide a simple proof showing that lower-semicontinuous functions that are locally Lipschitz continuous on their domains — functions playing a central role in nonsmooth optimization — admit Lipschitz continuous steepest descent curves in both senses.
Citation
arXiv:1212.1231 [math.OC]