Curves of Descent
Optimization and Control
2013-05-08 v2
Abstract
Steepest descent is central in variational mathematics. We present a new transparent existence proof for curves of near-maximal slope --- an influential notion of steepest descent in a nonsmooth setting. We moreover show that for semi-algebraic functions --- prototypical nonpathological functions in nonsmooth optimization --- such curves are precisely the solutions of subgradient dynamical systems.
Keywords
Cite
@article{arxiv.1212.1231,
title = {Curves of Descent},
author = {D. Drusvyatskiy and A. D. Ioffe and A. S. Lewis},
journal= {arXiv preprint arXiv:1212.1231},
year = {2013}
}
Comments
23 pages, 1 figure