Optimization Online


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

Modify/Update this entry

  Visitors Authors More about us Links
  Subscribe, Unsubscribe
Digest Archive
Search, Browse the Repository


Coordinator's Board
Classification Scheme
Give us feedback
Optimization Journals, Sites, Societies
Mathematical Optimization Society