Trajectories of Descent

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.


arXiv:1212.1231 [math.OC]



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