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Trajectories of Descent

Dmitriy Drusvyatskiy(dd379***at***cornell.edu)
Alexander D. Ioffe(ioffe***at***math.technion.ac.il)
Adrian S. Lewis(aslewis***at***orie.cornell.edu)

Abstract: 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.

Keywords: Descent, slope, subdifferential, evolution equation, semi-algebraic

Category 1: Convex and Nonsmooth Optimization

Citation: arXiv:1212.1231 [math.OC]

Download: [PDF]

Entry Submitted: 12/21/2012
Entry Accepted: 12/21/2012
Entry Last Modified: 12/21/2012

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